Hello there lads and or ladies. How's it going? It is Petrifying Pumpkins here. Today I have a conspiracy theory video that's kind of in the middle of going viral. I'd say by this time tomorrow it'll be everywhere but already it's kind of widespread. People are starting to pick up on us in the industry. Big names like Jason Schreyer and stuff like that are retweeting about us. Basically it's the big conspiracy that this independent studio who revealed that they're teaming up a PlayStation back in like April or something like that. Blue Box Studios that these guys are secretly not really a company at all. They're shell organization hiding the true identity of Kojima Productions and that they're working on a next Silent Hill or Reboose or whatever Silent Hill. This is important for us because we've I've already made two videos about Kojima working on Silent Hill. Both of them had to do with Vior support. Vior was heavily rumored for both of those things so that's why I think it's definitely worth looking at here but even if it wasn't Vior I'm a huge Kojima fanboy anyway so I'm like I'm loving this even if this doesn't turn out to be true at all which I think is going to be highly unlikely.  It's just we'll get into it. It's random, it's crazy but very very exciting. I wish more game studios would do these kind of a or g's I guess you could call them but I guess you kind of need someone like Kojima even if he's not involved he might not be involved in this at all it could be crazy. Anyway let's just get into it. Alright so I'm just going to pop up this Reddit thread here which is like okay so I was looking at a red thread yesterday that one got removed I don't know why it got removed but for whatever reason it got removed and it was copied and pasted into this brand new Reddit which is dedicated called the blue box conspiracy so or slash blue box conspiracy if you want to check that out yourself so this is where people are putting all the evidence together that something's not right here something's going on behind the scenes. Here are all the possible hints that blue box game studios is related to Kojima and Silent Hill. I think I might be a believer there are several points that hint towards abandoned which is the name of the game they were teasing I guess I should mention those they tease this game with like a minnest long gameplay trailer if even thus it was just like a first person guy walking around in the woods with a handgun and a bit of voice work was playing everyone kind of like looked at it they're like okay this kind of looks interesting enough too early to see or too early to tell or judge and then it kind of went off the radar for a biz even though this like was kind of speculated that I had something to do with Kojima even back then it's only really gain and steam recently with all this kind of crazy stuff I've tried to compile all the ones I could find for the moment okay so first things first the tweet that started this all let's take a look at that okay so this is what happened this tweet here which is what blew it up recently 15th of June which is three days ago they tweeted this guess the name abandoned equals first letter s last letter l reveal closing in so this revealed that the name of the game isn't actually abandoned that's like a working title or something and the first letter of the actual name starts with an s last letter starts with l obviously everyone jumped to silent hill you know I mean it could be other things like survival it's probably a bunch of other words out there that start with s and end with l there's no way they didn't think that's when they were putting this tweet out they couldn't have ignored the fact and of course everyone jumped on including myself you know and there's more hints and stuff down there this is a dangerous game friendo and all this kind of shit yeah so that got people in a frenzy rightfully so you should all be in a frenzy right now I'm in a frenzy Kojima used a fake studio when teasing both Metal Gear Solid 5 the Phantom Pain and PT so Kojima has a history of doing this shit first he did it with Phantom Pain with Moby Dick studios and they even had a twitter account and the twitter account would came out and denied us like they have denied it they're like oh we're not associated with Konami we're not associated with Kojima this is not Silent Hill we're sorry that we did this etc etc but the Moby Dick studio did something similar they're like I don't know why people are comparing us to Metal Gear Solid this is completely original or whatever so you can't trust that either and then of course PT which like just randomly dropped it was like at some kind of conference show it was being made by some studio like 77 Aziz or something like that and nobody knew anything about us and of course when somebody finished this the Silent Hill trailer came on the end so absolutely there's a precedent for Kojima doing something like this next up Abandon received a short teaser trailer on PlayStation's YouTube channel alongside a blog post hitting I guess he meant to say hinting for release laser this year Silent Hill composer also teased a new game revealed for summer 2021 which was shot down by Konami I remember this I think we talked about this in one of my other videos about this so they both line up together so that's another solid damn and evidence but it's you know it's lining up another clue the animated ps studios logo that plays ahead of first-party games glows blue for a moment creating a blue box so that's kind of a stretch the blue box logo thing boss there's a better one about the logo coming up soon blue box picture question mark this is from six days ago let's check this out honestly I don't know what's happening in this one I mean I guess there's a blue box in the corner of the images holding but that's that's a really stretch unless there's a translation here and that means something else but I'm not gonna go into that one there's too much more interesting ones to go into so another one kajima recently twisted with words silent and hill I did see this one this does seem suspicious I think was like a book he's reading these books and his thing here thanks harper books the silent wife by Karen blah blah blah blah blah then there's joe hills silent hills it's not even hill it's hills plural which is the name of the game that he would have been working on it is a bit suspicious and when did he tweak this June 9th I mean it's all happening very close together you know it's very suspicious next piece of evidence your honor there are no saved trademarks for blue box game studios but their traders claim there are or that they do have trademarks that's a red flag you know next up blue box game studios youtube banner is a bunch of hills yes it is let's check out their youtube channel I guess we'll subscribe to it while we're here and it is a bunch of hills and you can see well it's a cloud but you know you could see this as fog representative of silent hills now this could be like a stock picture like a default youtube thing but you still have to pick that so they like willingly picked this image again not diamond but another little thing you know next things up next things up next piece of evidence the blue box game studios logo is basically a playstation logo colors inverted and I believe somebody else pointed out that the fonts used are the exact same it's the same font so the studios font is the same as this font over here now I'm not a legal professor or whatever you want to call us but um wouldn't these fonts be trademarked by Sony a bit suspicious to use the same fonts in a profession a professional professional capacity like you know something being your actual logo maybe this is a publicly available font maybe you know I'm not going to rule that out but yes another point is that it's all inverted the colors as well where it's black here it's white here blue box is a term used for phone scams therefore this is a scam you know to try and let us know this isn't real it's a scam next up employees at company LinkedIn profile use stock fossils not real pictures of people their stock fossils very suspicious next up Jeff Keeley follows studio on Twitter but I think what's more important here is that this Twitter account their Twitter account only follows six people and one of those people is Jeff Keeley and of course we know that Kojima is super ties with Jeff next up at the abandoned trailer at the 49 second mark the letters P and T are covered by trees I actually didn't check this one out so let's do that together the letters P and T are covered by trees okay I see it here there's something written on the walls like killed the trespassers or something so the the T and the P are covered by this tree PT playable teaser second hills could be a clue that's that's one of the ones that could be maybe reaching a little bit boss I mean it's a very deliberate shot so we'll be framed with this way deliberately so you know next up a couple months laser blue box game studios reveal that abandoned will get its own ps5 app which would let players run the games trailers in real time on the ps5 this is a curiously specific thing that not even first-party PlayStation studios games have done so it raised some eyebrows that this unknown game studio will be the first to pioneer at the feature that's definitely weird and suspicious another game that got a console application as a teaser for an upcoming release but was laser abandoned quotations was PT I mean the evidence is all adding up we're going to get this app thing and apparently it's coming out in the 22nd of June which is only a few days away so we're probably going to know everything on the 22nd of June the twister handle for blue box game studios is BB game studios a possible death stranding reference if you don't know what that is the baby that Norman Reedus carries on his chest is a bridge baby and he calls it BB for like they're all called BBs in that game so BB game studio you know blue box tweeted in one of their tweets that their game would feature snowflakes of blood this was used in PT teasers I think this one was debunked as like an untill dawn thing instead so I'm going to skip that one a little bit blue box game studios appears to be founded in 2015 exactly one year after the release of PT and right around the time Kojima was going through his breakup with Konami so the timing adds up although this is like a real long con if this was been planned from all the way back in 2015 that's kind of I mean I don't know if it's especially if it's Silent Hill and he was in the middle of fighting with Konami then they sure they like they wouldn't have allowed this so the blue in blue box by the way what the blue stands for is revealed up here best level user experience so that's what blue box stands for that one's a bit weird to think that he's been planning this all the way back then with everything that was going on very strange next up blue box game studios only other game named the whisperer was completed by another studio and its icon is a black handprint just like in death stranding so the black handprints were a common motif in death stranding I don't know what this game the whisperer is so they actually have met other games I've heard about this but that these games are like impossible to find although maybe this one is easier to find because it was finished by a different studio or something I don't know one of their cancelled games named lost tapes is a soundtrack in Metal Gear Solid 5 so they were making a game called lost tapes and lost tapes is a soundtrack in Metal Gear Sam in the new death stranding director's cut trailer uses a backpack with the Netherlands logo blue box studios are supposedly based in the Netherlands can we see a picture of that okay there it is hmm now I was going to say that I'm pretty sure Sam and death stranding anyway there was like a red white and blue colors like that was Bridges colors like the name of an organization in the game so it wasn't weird to see that but the way it's laid out here like every time I saw it was vertical but here it's horizontal like a flag so I'd have to go back and see if that's actually how it looks since it released in 2019 I don't know so the guy who posted the blog on PlayStation like the director of this studio his name is Hassan Karaman and his initials are the same as Hideo Kojima HK okay keep that name in mind Hassan Karaman we'll come back to that most of the tweets made by blue box are at strange local time hours of around 3am the studio is claimed to be located in the Netherlands Kojima is located in Japan which is seven hours ahead in time so the times are weird if they're based in the Netherlands why are they tweeting at 3am 1am 2am all these weird times but those times line up to be fine in Japan early morning times Hassan Karaman has an account on PSN called Sneaky Warrior with the total number of trophies 1, 2, 3, 8 the same for the Japanese Silent Hill commercial Hassan had YouTube channel called 2727 Silent Hills was cancelled on April 27th bit of a stretch that one I think Sneaky Warrior played a game that isn't available on the PS store that is using Siren Head as an image Junji Ito reacted to Siren Head a few months ago and implied about working with Kojima let's look into this one let's get to the bottom of this one this is his profile Hassan Karaman and he recently played this game Demon Blood and it has a picture here of Siren Head played it two months ago for a total of one hours and this game doesn't exist apparently so that's suspicious and Junji Ito I do remember him complimenting Siren Head on Twitter not too long ago so that adds up next up this is the big one that blew my mind you know so Hideo his name translated from Japanese to Turkish means Karaman it's the same fucking name as your man which is the last name of Hassan Karaman the head of blue box games both of their names mean hero in their respective languages and here's something I looked up which I didn't see anyone else do there okay so Hassan translated this mote imasu right so flip it around and translate that into English and you guess I'm waiting suspicious I think especially Xena's Kojima's catchphrase and all the Metal Gear Solid games where I guess Snake's catchphrases kept you waiting huh you know nobody seems to be talking about that I've posted in the comments of all these threads but you know I guess some genius goes on noses that's fine next up Hassan Karaman does have an apple app store profile with a bunch of low quality acid flipped games under his belt the only app that's not a game is called go fit XL which sits under the health and fitness category the description of this app says at one point personal training PT programs no I'm not into my personal training so I don't know how often personal training gets abbreviated to PT like that it's suspicious okay so that's all of the stuff that's been added but I think other people in the comments including myself have been adding other things as well so this is from Daniel Dwyer who's actually kind of big enough in the game and media like report an industry he does the no clip stuff and giant bomb or he used to be game spot I think so he says didn't see this mentioned but Kojima has strong ties with gorilla games in Amsterdam not only did they give him the Decima engine that that stranding will laser be built on but a bunch of their devs worked on dead stranding also worth considering that the current head of PlayStation Studios was running gorilla at that time so if anyone wanted to accommodate Kojima's crazy marketing schemes and work closely together with PlayStation to make that happen it will be Kojima and Herman Holtz them guys are tight you know so that could allow all this stuff to happen so this person here says that the flag is always there it's not just in the newest trailer so that netherlands flag even though it's not really supposed to be a flag I think in the game might not be a clue at all okay so this one from Shave2 says okay this is big blue box game studios is from Leiden Johan Huzinga the author of the monograph homo Ludens so whom homo Ludens was like a big thing team or something for dead stranding that was always brought up so this person who invented homo Ludens that phrase or saying or whatever was a professor at Leiden University suspicious that should be added to the thread that's pretty suspicious so I agree with this person the chances of all these facts being coincidental is astronomical it might be more impressive for this game not to be some kind of Kojima thing if this turns out to be actually just a game called abandoned by a real studio called blue box who are in indie studio that might blow my mind now at this stage more than anything crazy being going on you know keep in mind in the previous videos I did where there was sources from insiders who leaked certain things Vior was very much in the you know in the conversation and it was always next gen Vior so this game I know this game is supposed to come out in 2021 the end of this year might not make it then but then there was there was talk about there being two different silent hills coming like one of them was a reboot and then another one was an episodic kind of a thing and I think Kojima was supposed to be behind the episodic thing it's hard to keep track of it all anyway I just love this conspiracy stuff looking up all these clues I like being here for it now you know this will probably all be revealed by next week and then all the fun will be over but until then I'm enjoying the fun right now so if you want to look into us I'll put the link to this thread in the description maybe you don't care at all that's fine whatever yeah but this could be a really cool Silent Hill game or even if it's not Silent Hill it's something cool coming from Kojima which fingers crossed will come to not only ps5 but psv or two or ps5 or whatever they call us you know feel free to let me know if you think I'm nuts this is nothing a lot of people think this is nothing but to be honest I think if you think this is nothing you're more nuts than the people who think this is something you know at this point it's too much too much coincidence anyway gg stay moist etc etc


Good morning and welcome to church. He's ready. Who else is ready to worship this morning? Yeah, amen. Yeah, let's go Well father, we thank you for the privilege that we have to worship God Remind our hearts this morning of the blessing that it is to come into your presence Lord. We come Ready to give you praise to give you worship Lord our hearts are ready to worship this morning We recognize your greatness in the sanctuary Lord We shake off the heaviness of the week every distraction I silence in the name of Jesus and Lord. I thank you for who you are We set our attention and our affections and our focus on Jesus the one who seated at the right hand of the father Jesus you worthy of our worship. We love you. We bless you in Jesus name The sound of the Savior's robe as he walks into the room Where people pray where we hear praises he hears There is a sound I love to hear is the sound of the Savior's robe as he walks into the room Where people pray where we hear worship he hears Praise Allah sing his praise Allah Sing his praise Allah Sing his praise Your presence that's here Jesus all across this room just open up your hands with me and close your eyes and Take a minute to just recognize the presence of God the word says that Wherever his people are gathered wherever they sing his praise. He's there in the midst Jesus we just take a minute to recognize your presence. I hear to just sing some songs Lord We're here to bless your heart. We're here to tell you just take a moment and just sit Praise the rise whether it's just your great or your beautiful or in the bridge just begin to tell I know you say voice to sing that bridge again We're just gonna lift it to the Lord his praise that he's worthy He's holy and that he's never left us and forsaken us But God praise and our love for the Lord this morning God we give you our love we give you our praise Give you the honor and glory that's due your name because you alone are worthy of it Receive it receive it this morning from your children and your people in Jesus name. Amen Amen, you can go ahead and have a seat if you would radiant church. My name is John. I'm Campus pastor here in Richland, and we're gonna Continue worshiping and continue in our service with something that is so Impactful and such a part of the culture and DNA of radiant church. We're gonna have child dedications and I think First of all, one of our core values is that we're family-oriented we're word-centered spirit-empowered Family-oriented kingdom focus and mission motivated. So those are our five core values. And so there is a Biblical mandate for family and for children and Psalm 127 says they're actually gift from the Lord And I think it's so significant that as we're kind of all experiencing this Impactful and and quite radical shift in our Supreme Court and in our Government and in the protection in the lives of the unborn. Yeah, we it's great. It's incredible We're so grateful for that We're so grateful that God's moving and I believe it's really a sign of of revival that's to come But I think it's also incredibly Timely and impactful that we're going to have children dedicated to the Lord on the very weekend that that took place here at radiant church And so we don't baptize infants It may come from a background Maybe you're visiting and we're not here to say you shouldn't or you can't what we see in scripture is people are baptized It's a decision they make subsequent to salvation to receiving Jesus but in the Old Testament Hannah gives birth to Samuel and she brings him to church She brings him to the temple and she has the leaders and the people in the church bless Samuel for the work of the Lord and so that's what we're going to do And we have some parents who are going to bring their beautiful children up here And we as a church and as a leadership are just going to pray and we're going to believe God's Blessing and favor to be upon them and their family. So when I call their names I'm going to ask you to just give them a round of applause and then they're going to line up here in the front And we've got quite a few today because we're building this church the old-fashioned way So I'm going to put my readers on so I have a 86 percent chance of getting the names right here We go very professional. Okay, Austin and Jenny Beef is if you would bring up Jaden to the front here and line up. Let's give them a round of applause Ryan and Kate tomorrow if you'd bring up Baylor Ryan to the front Thank you Daniel and Alexa Dorn if you'd bring up Marissa Naomi reasoner Sophia and Ruth May to the front here they come Danielle Evans if you'd bring up Aria Marie to the front well and Rachel Evans if you'd bring up Leon James To the front here comes Leon Chris and Megan foe if you'd bring up Jameson John to the front Adam and Morgan Hammond if you bring up Hadley May and Olivia Rose Here they come Tyler and Rachel Johnson if you'd bring up Forest Lee to the front there they are Kevin and Sarah not been if you'd bring up Tyler Joseph to the front here comes Tyler Nate and Kristen Rybal if you'd bring Brooks to the front here they come and Last but not least Tyler and Kate Rominger if you would bring up Griffin Jay to the front. Let's give them all a big round of applause We're my way around here Again, we're excited We're honored to partner with you as you dedicate your children to the Lord There's something so impactful about making this decision and having your children be Brought up in the house of the Lord and then the ways of the Lord And so it's our honor is radiant church to partner with you and to celebrate What God has done in your families and so I'm gonna ask you some questions as mom and dad I just want you to respond with we will with God's help and then at the end we'll pray So first I want to ask to you as parents Consecrate yourselves to the Lord today to help your children walk out the plans and the purposes God has for them If so say we will with God's help Secondly, are you making a decision today to dedicate your children? Recognizing that according to Psalm 127 they are a gift to you from the Lord if so say we will with God's help Lastly, do you accept the responsibility as parents to teach and to train your children in the ways of righteousness? That they would love God love God's word and love God's people if so say we will with God's help and Congregation I'm gonna ask you it's a church. We're a body of believers to you as Those who are worshiping with these families promise to pray for them come alongside of them and help them and their Children walk in the ways of the Lord if so say we will with God's help I'm gonna ask you if you would to just extend your Hands towards these families and these children and we're gonna pray for them father right now. We recognize Like every single child is a gift from you God that you are the giver of life You are the author of life and God your word says that these children were known by you Before they were even in their mother's womb and God you knew them you called them You have given them plans and purposes already and God we speak to their lives We speak to the destiny and callings you have for each of them right now God we declare David's God and Daniel's esters and roots are coming up those who would make an impact in the kingdom of God with righteousness and grace and truth God and we surround them with our prayers and we say God let your hand of Mercy and grace be upon them God and we ask that every single parent would have the wisdom and have the grace and the Ability by the Holy Spirit to teach and train them in the ways that they should go and your word says in Proverbs when we do as they grow old They will not depart from it and we stand on that promise in Jesus name Amen, amen last thing and this is important. We have a tradition here at radiant church based on the greatest children's movie of all time where we have Mufasa showing off Simba on pride rock to the Congregants that have gathered so if you guys want to can our physically able you can raise your children up and let's give them all a huge round of applause Amen Amen congregation if you would stand on your feet and as they go back to their seats make sure you give them a high five tell them Congratulations say hello to a few people around you when we'll continue with our service Welcome to radiant church. Hey, let's give another round of applause So our families that are here this morning with us. Thank you so much It's beautiful. It's beautiful. Well, again, everyone. Welcome to radiant church We exist to lead people to become radiant disciples of Jesus Christ My name is Tim and I have the joy of serving as one of the pastors here And if this is your first time here or your first time in a very long time We're just happy that you are here with us before our first time guests in the seatback pocket in front of you You'll see a QR code feel free to scan that We're just gonna ask for some basic information so that we can stay in contact with you and for those who a little bit more extroverted We invite you to fill out that communications card make your way at the end of the service to guest central We have a special gift that we want to give you just to show you that we appreciate you for being here with us Hey church, let's give a round of applause for our first time guests as well. Thank you so much For being with us today today Awesome well at this time I want to invite the ushers to come forward to receive today's tithes and offerings now We have been in this fundraising campaign called Kingdom Builders as a church We are mission motivated and we believe that our giving can advance the kingdom of God And I want to give you guys an update just in the last couple of weeks you radiant church as a family united has given $750,000 to Kingdom Builders That's specifically going to India so that we can build a school to help brother Abraham Thank you so much for your faithfulness and you're giving now the goal is 800. All right So if you have a $50,000 check, please make it up. No, um, but for real though The goal is 800. We are almost there now Let me remind you some of you may hear this the first time the original goal was 300,000 Look how much you've given Praise God for his faithfulness as a church We want to say thank you so much for your generosity believing that your kingdom dollars Actually goes so that souls can come into the kingdom amen amen So I'm just gonna pray for us that God will continue to use us as a church to be generous To the work that he's doing. Let's pray father again. We do love you. We thank you for today Holy Spirit give us cheerful hearts to give to you God you've given so much to us And so we just joyfully give back everything that you've given to us God We pray that you would prepare us even as we hear the word of God being preached today from pastor Garrett Holy Spirit Fill him. Thank you for bringing him to our church the blessing that he's gonna be and the blessing that he is We now are ready to hear from you. It's in Jesus name that we pray and everyone said amen Everyone welcome to radiant. My name is Preston and I'm Jackie and this is radiant news Being water baptized is the outward proclamation of a decision to follow Jesus if you're a Christian But you've never been water baptized consider. This is the next step in your journey We're hosting water baptisms at our weekend services on Sunday July 31st in Portage and Richland and we encourage you to register The radiant city vision is moving ahead and we are so encouraged by all God is doing through your faithfulness and generosity Check out this special radiant city vision Hey guys pastor Sean here, and I am so excited to tell you what is happening right now at our radiant city center location Back in September 21 We launched our prayer room where we now host 15 prayer meetings a week and broadcast five of them online We're continuing to optimize this space with additional video technology and infrastructure So that we can launch our Sunday morning services here and continue to host our weekday prayer meetings seamlessly We're so excited to be able to bring weekend services to the heart of this city beginning in the fall Thank you so much for your continued partnership for helping us build radiant city You can find all this information and more at radiant.church last weekend. That's it for us. Thanks for following There it is I've been waiting for that intro for weeks now for my opportunity because I Don't it just gets me going it gets me going. Good morning. Beloved. How you doing? Awesome, my name is Garrett and I have the privilege of serving as one of the pastors here at radiant church It is good to be with you this morning. I want to extend a special welcome to our family in Portage, it's good to be with you as well. I am excited about today I have been fired up. I've rewritten this sermon 37 times maybe 38 I don't know somewhere in there, but I have the incredible honor today to Teach the next installment of in our wind and fire series and I have titled today Something very masculine Very very masculine all the men in the house are gonna get excited about this Just right off the bat you're gonna see it and you're gonna get fired up like gladiator It's called disciples and dandelions. Come on.  Let me see the Bible because this is encouraged me Portage. Hold it up there, too I love it. I love it. I love seeing you bringing your Bibles to church Acts 11 is where I will be teaching out of today starting in verse 19. It says this Now those who were scattered because of the persecution that arose over Stephen Traveled as far as Panisha and Cyprus and Antioch Speaking the word to no one except the Jews But there were some of them remember that some of them Men of Cyprus in Cyrene, and you know, I just got let me pause there I did not intend on pausing there, but I just I'm a Bible teacher and I have to stop Because right now in America, we have a major epidemic We have a major epidemic and its infection is in the church I'm not talking about the season that we've gone through but we're still kind of in but the tension We don't know how to deal with yet and all of like should we say something should we not should we talk about this? I don't know. It's the awkward thing in the room right oftentimes, but this says something that I want to point out it says men of Cyprus men of Cyrene Now I'm not wanting to point this out at the exclusion of anyone, especially women But I'm wanting to point something out here. We are about to see a major event take place in the book of Acts a major event that has its effects and recourse on our lives here today and I believe I Strongly believe that a major reason for the event that we are about to read about that We are about to see that we are about to begin praying for I believe a major Catalyst to this event is because there were men of Cyprus and men of Cyrene who stood up in a culture that didn't want men to stand up and they preached the word of God and I believe that God is calling us to do that men and So men I'm calling you To stand up We've been sitting for too long We've been hiding in man caves for too long. I Hate man caves if you have one. I'm sorry. I don't like it I don't like it because you're not called to have your own room separating from your family So you can do what you want when you want to play video games all day There's a reason why we laugh at the movies where we see a grown man arguing with a 12-year-old because it's ludicrous and Some of us are doing that I believe God is calling us out today Out of the man cave and back to the forefront of our family where we lead well Where we lead strong where we actually do what Pastor John said train up our children in the way that they should go when they're 18 go like Some mom and dad can get their beach house, you know Their lake house on goal or any I don't know it. I'm just go Lord send you I'm Joe. I'm joking, you know, but I Believe that I believe that God is calling men of Richland Men of Portage Men of Kalamazoo men of Plainwell, Otsego battle Creek Grand Rapids I believe that God is calling men to stand up So he says men of Cyprus and Cyrene on Who coming to Antioch spoke to the Hellenists also? Preaching the Lord Jesus and the hand of the Lord was with them in a great number who believed turned to the Lord The reports of this came to the ears of the church in Jerusalem and they sent Barnabas to Antioch When he being Barnabas came and saw the grace of God, he was glad now. I love this because Barnabas was intimidated by What was happening there and not happening where he was in Jerusalem? He wasn't in competition with these people. He celebrated with these people. He didn't know them They hadn't been in class with him. They didn't go to the to the Barnabas School of Ministry He was excited. It said he was glad he was excited. So he celebrated and and so it says And when he came he saw the grace of God He was glad he exhorted them all to remain faithful to the Lord was steadfast purpose verse 24 for he being Barnabas was a good man Full of the Holy Spirit and of faith now I want to mention I want to make a special note here says he was a good man full of the Holy Spirit and faith Listen, you don't get the Holy Spirit because you are good Please hear this You don't receive the Holy Spirit because you are a good person The Holy Spirit is given to you and he begins to make you good Goodness is a fruit of the Holy Spirit in the life of someone who follows Jesus Okay Galatians 5 verse 22 you should check that out later on. I don't have time and a great many of people were added to the Lord so Barnabas Went to Tarsus to look for Saul and when he found him he brought him to Antioch for a whole year They met with the church and taught a great many people. What was happening there? they began discipling and Antioch the disciples were first called Christians and in these days prophets came down from Jerusalem to Antioch and one of them named Agatha stood up and foretold by the Spirit that there will be a great famine over all the world This took place in the days of Claudius So the disciples determined everyone according to his ability to send relief to the brothers living in Judea and They did so sending it to the elders by the hand of Barnabas and Saul as a whole Acts 11 is devoted to a major Foundational event of the early church. This is true both ecclesiastically meaning as it pertains to the church and Missiologically as it pertains to the mission of the church and it starts off We didn't read it, but it starts off with verses 1 through 18. Okay with the Apostle Peter Reporting to the church at Jerusalem. What happened there in the previous chapter acts chapter 10 and that event that the Apostle Peter is reporting on and about is an event that actually inaugurated the early church's mission to the rest of the world to the Gentile world immediately following this we come to verses 19 through 30 and and and and it says and basically what happens I should say is we are brought to ground zero of the mission that Peter started Unfolding and it's unfolding in a city in a place called Antioch And the way by which we get to Antioch and the way by which this incredible global mission Begins to unfold in this place called Antioch is completely Providential it says because of the persecution that arose over the death of Stephen Disciple, I'm sorry. Yeah, Stephen disciples of Jesus fled great distances for their lives and Similar to how the seeds of a dandelion are scattered by the wind Disciples of Jesus were scattered by the persecution in their land Some as far as Cyprus and Cyprus was about 250 miles away and and it included a boat ride Some as far as Venetian Venetian was about 190 miles away. I Dug in deep and because I'm a Bible nerd and I like to read on this stuff and go deep into it I like to look at maps and stuff like that and and so I started looking at these distances and and then I dug deep into Commentaries and most scholars actually Conclude and and they're almost in full agreement that it took uber over eight months to get everyone to Phoenicia Okay, and to the island of Cyprus uber was built just by this one event but seriously Really think about this because we read These texts and we are so distant from them and we are so removed from them that we actually Don't realize everything that Happened and we don't realize all the energy that it took in and all of the pain that probably and had to take place When these kind of things happened think about this think about how far they fled Think about how long it took Think about how arduous it was for these people physically spiritually emotionally Think about the fear the worry the uncertainty that these people carried as they scattered as they fled for their lives and Yet it was in these conditions It was in these conditions It was this place and those people and these circumstances that God used to launch this mission and Antioch was the perfect setting for it the perfect setting for the early church to begin its mission to the Gentile world You see Antioch was the third largest city in the Roman Empire There are roughly 500 to 800,000 people in the city of Antioch It was it was third only to the great City of Rome and to the great city of Alexandria Antioch was a significant port city along the Orantees River and it had a had a strong trading and Strong commerce market. Okay. It had fertile lands. The lands were were known to grow great Great producting and great groceries. Okay Antioch was influential. It was influence and it was advanced for its day and then there's another Biblical reality woven into the fabric of Antioch that is nothing less than providential and it is this fact Antioch had a large established Jewish community present. You see verse 19 part B said they spoke the word of the Lord to no one except the Jews. This is how it started and as I As I studied this week and as I prepared this week and as I tried to step back from the text and build a Panoramic image if you will of what was taking place in Antioch the Holy Spirit kept bringing to the forefront of my mind this one particular verse From Romans Romans chapter 1 1 verse 16 the apostle Paul says for I am not ashamed of the gospel For it is what is the gospel is for it is the power of God for salvation For some No, for everyone remember this word everyone for everyone For everyone for everyone who believes but this is why I said it's providential because it says to the Jew first But also to the Gentile What a wonderful word the apostle Paul used there everyone everyone Everyone if you look up everyone in every language it means everyone. It's amazing how that works Everyone there's no there's no translation needed everyone Everyone what a wonderful word the apostle Paul used there because what we find happening in Antioch is the gospel is going out to and it is reaching everyone Jews and Gentiles it is reaching everyone, but also What a wonderful word for us today for those of us who feel Or think or maybe have been told that there's something about us that actually rules us out that it's for everyone But us it's for everyone, but me Wrong family wrong background wrong history wrong side of the tracks wrong education wrong language wrong culture wrong decisions Wrong job wrong neighborhood wrong place wrong skill set wrong time wrong insert The wrong that you have been told or you have felt or you have thought here, but then But then like our brothers and sisters in Antioch We hear the gospel the good news that says everyone who believes Everyone who believes I want to go back to our text and I want to zoom in quickly on three particular verses verses 19 through 21 Just to read it one more time to bring it back to our attention. It says Now those who are scattered because of the persecution that arose over Steven traveled as far as Venetia and Cyprus and Antioch Speaking the words and no one except Jews now. Here's where I really want to hone in But there were some of them men of Cyprus and Cyrene Who on coming to Antioch spoke to the Hellenists also preaching the Lord Jesus And the hand of the Lord was with them and a great number who believed turned to the Lord Now this passage it takes us actually back into Acts to a few to to Acts chapter 8 Acts chapter 8 verse 1 It brings us back to this because this is what it's speaking about Acts chapter 8 verse 1 says and there arose on that day a great persecution against the church in Jerusalem and They were all scattered throughout the regions of Judea and Samaria now get this except the apostles So let's do a quick recap. Let's let's let's put framework around all this real quick acts 1120 said some of them Acts 8 verse 1 said except the apostles Except the apostles I Want I want I want that to stick out in your mind today And I want you to leave realizing what took place at Antioch today You see because I find this interesting. I find it interesting that this great thing takes place And the apostles aren't even there The trained professionals Aren't even there. They're not even there What we see Happening in Antioch. Let me be just a little bit more specific the revival that took place in Antioch The church that was started built in Antioch This was not Peter and John being sent to Antioch to preach the gospel This was not Philip and James being sent to Antioch to preach the gospel This was not powerful technical preachers and prolifically trained pastors Being sent to Antioch to preach the gospel This was not them our text teaches us that this was unnamed men and women of God Christians With no church planning experience and No cemetery degree. I mean seminary degree. I say that every time Seminary degree, I'm sorry. No seminary degree. They had no stage. They had no mic They had no smoke. They had they had no place to meet. They had no programs. I mean They didn't even have an actual plan in place all they had was Jesus So they preached Jesus to everyone To everyone, but why everyone why? Because everyone who believes Everyone who believes I Don't know if you know this but This goes against every Western church strategy and growth model today This goes against at all I mean if you want to grow a church or if you want to plant a church today get a good communicator some good musicians a good place to gather and Set some good programs in place and you're pretty much good to go You're pretty much good to go and it doesn't hurt if you get some of those tall inflatable tube guys just sit out front in the parking lot and Do this whole thing and you put the name along the sides. It looks like he's wearing merch or something like that Yet, I don't know. We just read it None of those things were present at Antioch None of them were Understand church, none of these are bad None of these are bad. In fact With the right heart and the right intention. They are all in fact good They are great They are awesome, but beloved. I don't want us to miss this this morning Instead of professionals places and programs at Antioch what we find are some people Some people It was just some people verse 20 Some people who fled for their lives and ended up in a place called Antioch and these some people were so in love with the Person of Jesus They were so consumed with Jesus Jesus wasn't actually he was actually enough for them They were so in love with Jesus they would start one of the greatest revivals and churches in the history of Christendom they were in love With Jesus. Are you getting this portage? Please help me like we're quiet over here in Richland Please help me portage like portage. Come on. Help me. I don't know if you're getting this. I'm because I'm talking about ordinary nine to five men and women disciples of Jesus Christians preaching the gospel to everyone Preaching the gospel to everyone in verse 21 says the hand of the Lord was with them all and a great number of Them turned to the Lord because of it ordinary nine to five Men and women of God who just so much loved Jesus that they wanted to tell everybody They met about Jesus in other words that church at Antioch was a church where disciples were making disciples Disciples were making disciples. You see they were like dandelions Dandelions and the fact that wherever Wherever they were blown to they planted their seed in the soil and their seed was the gospel of Jesus For it is the power of God for salvation for everyone who believes it is Now This is where acts 11 confronts the majority of the Western church today And I don't know if you heard me, you know about two months ago preach But I mentioned that I like I just I have a little bit of a confrontational spirit in me like I Confronts and You can just make this is actually when you might want to just look at the person next to you and say he's gonna do it He's gonna do it Lord help me this may come as a shock to you But sorry that I'm not sorry It's not pastor Lee's job to love your neighbor. It's your job. Please hear me. It's not pastor Lee's job to reach your neighbor It's your job. It's pastor Lee's job like every pastor's job To help you to counsel you to train you to equip you to encourage you to pray for you, but Make no mistake as a disciple of Jesus as a Christian verse 26 and In Antioch the disciples were first called Christians as a Christian. It's your job God didn't put pastor Lee on your street He put you on your street. I didn't put pastor Lee in your place of work. He put you in your place of work He put you in your place of work. So as a Christian It's your job and just so you don't think fake news Exclusive today Let me just let's just turn in our Bibles real quickly to the book of Ephesians chapter 4 Ephesians chapter 4 starting verse 11 Says this and He being God being the Lord he gave so when it says he gave what comes next are the gifts that he gave He gave the apostles the prophets the evangelists the shepherds also means pastors and Teachers so he gave them what did he give them for a pastor here? I'm about to tell you to equip the saints for the work of Ministry for building up the body of Christ until we all Until the pastoral staff. No, no, no, no, no until we all until we all Attain to the unity of the faith and of the knowledge of the Son of God To mature Manhood that in the Greek means a full grown bearded man bless Me oh Lord To the measure of the stature of the fullness of Christ so that we may no longer be children. I Don't know about you, but I turn on social media and all I see is children today Grown-up children Going to stores and I hear people arguing over stuff acting like three-year-olds having tantrums on the floor because mom didn't get him a gumball this time Tantrums children, but here scripture says he is calling us Out of that an Intumaturity so that we may no longer be children tossed to and fro by waves and carried about by every wind of doctrine Can you feel the winds of doctrine in our culture today? Can you feel them can you sense them? Can you see all of the doctrines blowing about that are carrying our brothers and sisters away and things that have nothing to do with the Gospel putting according to things that have nothing to do with the gospel Carried about by every wind and doctrine by human cunning by craftiness and deceitful schemes rather speaking the truth in love We are to grow up. I hear the spirit of God saying radiant. It's time to grow up It's time to grow up In every way into him who is the head into Christ from whom the whole body joined and held together by every joint With which it is equipped. How does that get equipped? evangelist pastors and teachers Equipped when each part is working properly.  I slept on this shoulder wrong and this arm was numb It wasn't working properly for like the first half an hour Like it just like I was like I Looked like one of those way of you guys in the shower. I was like come alive, you know I feel like we have a lot of parts in the church that aren't working correctly It makes up the body It makes the body grow so that builds itself up in love Now that we've seen my My confrontation if you will In scripture, let me just poke a little bit more I want to be fun.  It's it's my favorite thing to do I love to get to pray with you. I love to get to pray for you We love doing it and we take it seriously, but understand It's not because we are pastors. It's not because it is our gift It's not because it is our calling but because we are Christians and it's our responsibility as Christians of pray as Christ prayed It's for all of us it's for every single one of us to do we are to pray just like Christ Prayed the word Christian. I don't know if you know this when you break it down When you break the word down the I a in What that means is it means belonging to the party of belonging to the party of what preceded the I a in so belonging to the party of Christ That's what Christian means. I belong to the party of Christ. I am one of his people Okay, and so it is our responsibility as Christians to pray and this is why we have The radio city city center. This is why we have a prayer room where we gather Monday through Friday 8 a.m. Noon and 6 30 But listen make no mistake. This is not a time and a place For pastors to pray. This is a time for us to pray It's a time and it's a place for us to gather to cry out to God For a move in this area just like he moved in Antioch.  He said in no other way Can the believer come become as fully involved with God's work, especially the work of world evangelism as in? intercessory prayer There is no greater thing. This is the biggest part and so I Love that you pray at home, but something happens when we gather together in an upper room and we cry out to God We sing and worship We fall on our faces and we so in tears so that we may reap enjoy Something happens Something happens and so I want to Poke all of you and say get to the prayer room men Get to the prayer room start leading there I would love you men to join me Mondays at 8 a.m. Every Monday 8 a.m Join me Join me Join me Join me Understand beloved like we see happening in Acts 11 with the church at Antioch Radiant church exists to make radiant disciples of Jesus But please note that we do not exist so pastor Lee can make or will make radiant disciples of Jesus But so radiant church meaning the people of Radiant will make radiant disciples of Jesus That doesn't exclude pastor Lee from making radiant disciples that includes all the pastors and all the staff But it also doesn't exclude you The point is this it's not pastor Lee's job To make your neighbor your co-worker your boss your classmate your friend your family or your cat a Radiant disciple of Jesus. It's your job It's your job Beloved like a dandelion fills fields with more dandelions so disciples of Jesus are to fill the earth with more disciples Which should not surprise us because remember what Jesus's last words were before he ascended in Matthew 28 verse 19 go Go go get on the move go therefore and make disciples of all the nations He didn't say hey pastors go make disciples of all the nations. He said no no no go my disciples go go and make Disciples of all the nations but pastor Garrett. It's great. I Like it. I hear you But you don't know my neighbor You don't know my boss. You don't know my co-worker. You don't know my uncle Darrell if you knew my uncle Darrell their mess and Angry and I'm just gonna be real. They're evil, but pastor Gary. You don't know you don't know my place of work You don't know my city. You don't know my neighborhood. It's dark. It's difficult. It's evil You know that may be true I may not know all of those facets and all those details and all those inner workings of everything that you have going on in your life I get that so I'll give you I'll give you that one. You can have that one on me have a participation trophy for the day Okay Those may be true But can I tell you something? If not too bad. I'm going to anyways Antioch was no garden of Eden Antioch was no garden of Eden Antioch was a place that was known for literally its dark luxurious immorality It was a place that would discuss most of us today without vile it was and yet This was the place and those were the people that God chose to use the some of them The some of them to do this incredible work that we marvel at and we named churches after today So I say to you that this is the place and these are the people And these are the circumstances. Let me say it again This is the place and those are the people and these are the circumstances which I believe God is going to do and another Incredible work in and with just like he did at Antioch right here in this place and at this time But here's the caveat. Here's the thing You you you you have to do it just like some of them did it Because the hour that we are in right now is the perfect setting for it There's this little tick-tock thing going around it's on Instagram too and it's this voiceover that people put over the workout that they're doing 75 hard and all these kind of things. It's it's great, but the voiceover says this it says It says you can never get upset But about the results you didn't get By the work that you didn't do church We can't get upset About the results that we're not getting By the work that we're not doing He said go into all the world and preach He said proclaim the good news and in the gospel mark the word is proclaim the good news Proclaim the good news Proclaim it Beloved God wants to use everyone God I'm sorry God wants everyone to come to the saving knowledge of Jesus Christ But understand he is not looking for professionals to help make that happen He is looking for some of them He's looking for some of them He's looking for unnamed unnoticed unfollowed on Instagram Men and women he's looking for disciples Christians to help make it happen And I believe that when some of them step up here like some of them stepped up there What happened in Antioch it will happen in Richland it will happen in Portage It'll happen in Plain Wall outside go it'll happen in Battle Creek. It'll happen in Grand Rapids It will happen in your city and maybe I didn't name I Live in Augusta it'll happen in Augusta It'll happen in your neighborhood It'll happen with your neighbors. It'll happen in your place of work It will happen in your family.   Are you or are you not? Are you scared of the backlash that someone might say to you? Are you scared of someone filming you and putting it up on the internet? Are you ashamed of the gospel? I'm not I stand with Paul Because I believe I don't just think I Believe I know that it is the power of God for salvation For everyone who Believes I believe more now than ever That everything that we are going through everything we are facing all of the pressure That we are experiencing daily and all of the noise and all the traffic that's coming into our heads and our minds and consumes Us and is pushing us back. I believe that we sit in a perfect environment just like Antioch was a perfect environment. I Believe that God is Looking to his church saying Will you be some of them in the midst of all that? In the midst of all that turmoil and confusion and chaos Will you be some of them some of them Will you stand with me? I really hope and pray that you hear and you see even me as I point my finger that you see it all Not as an accusation But an invitation I'm not accusing condemning But I am drawing a line in the sand Saying it's time for us to get back to what we are called to do to begin with I Don't want anyone to feel condemned today, but I want everyone to feel challenged today And I want everyone to feel convict today because as I wrote and as I prayed and as I studied you can ask my wife even 20 minutes before we preached before I preached I was in the back going I hope no one gets like too pushed by this like Instead of encouraged they the enemy breeze lies on to it like I don't want that What I want is all of us to stand up and Be who we're called to be and do or call to do we are called to make disciples We are called all of us in this room if you are in Christ you are called to make disciples of Christ You are called and we want to help you And so if you don't know what that looks like you don't know where to start let us help you There's a lot of us around let us know we have a lot of awesome things in place to help you grow and Help you walk in the fullness of your calling right where you're at right now. And so let us know Come and talk to us. I Want to invite our prayer team and ministry team up to the front and as they begin to come up if If you don't even know the Lord you just are you feel far from the Lord Yet you feel this tug on your heart you feel the Holy Spirit saying hey, and you're one of them. I Just I don't want to What I want to do is I want to actually to ask you to do me a favor And I want you just to if you're feeling led by the Lord to say I surrender my life And I feel the Holy Spirit this this nudge in my heart this pulling this gripping of my mind I feel something happening inside of me I want you to do something. I just want you when I just miss in two minutes to come to the front and Talk to one of our prayer partners right here. Let us pray with you. It will be the greatest decision. You've ever made in your life Also, if you're in this room today, and you're saying like hey pastor Garrett, I want to step up But I need prayer. I need some courage. I'm pretty beat up. I'm pretty defeated.  We love you. We thank you for your word today Lord, I pray that all of us Would take this mandate seriously and we would go into all the world that we would go into all the world where you have us Into our city Into the grocery store into our place of work that we would take a stand in our families and we would make disciples of all the world Preaching the good news the gospel of Jesus Christ Lord, I pray that we that our lives As we look back on them that we would see a field full of disciples a fieldful Lord We would see family members and we would see co-workers and we would see people that we just met in the store and we would see Just tons and tons of people Lord for you are worthy of it. Lord. You were deserving of it So Jesus I pray for strength and courage in this room that as we leave here today that we know that we are not leaving But we are going we are being sent as messengers as carriers are witnesses of Your gospel of your good news For it is the power of salvation for everyone who believes Lord the grass withers the flowers the flowers fade, but your word stands forever We rest in that today in Jesus name. Amen. If you need prayer for anything, please come up You were dismissed. See you next week. Go into all the world


And the Centre for Migration Studies, Nandia Zikwe University, CMS now held its first international conference with the theme Nigeria and Migration today, the diverse strategies of state and non-state actors, as the ASIL Secretary-General Unizik Oka Anambri State speaking earlier. The Director of the Centre for Migration Studies, Professor Tresi Uto Asia-Juji, noted that the Centre for Migration Studies, Nandia Zikwe University was commissioned in the 28th of August 2018 by the Honourable Federal Commissioner, National Commission for Refugees, Migrants and Internally Displaced Persons, Sadia Umar Farouk. If one is migrating, one has to know, why am I migrating? What am I going to do in that country? What skills do I possess when I get to that country? What skills am I offering them? Migration shouldn't be a compulsion for anybody because when it's done properly, you know, there's a lot of potentials. If you look at a lot of countries, you know, they've understood that they've created legal pathways for people to be able to explore and, you know, welcome to come back anytime they want. So just like, you know, any migration expert, I'm an advocate for safe, orderly, regular migration, people should be able to move anywhere. But the host country, the receiving country and the country of origin and even the migrants should be able to, you know, benefit from the whole process.


As I mentioned in the last lecture that we were calculating the expected values of the I gave the expressions for the expectations or the variance etcetera of the order statistics when the sampling is done from a uniform distribution. I also mentioned that it is quite complicated to obtain the same expressions for the general distribution if the sample is from a general continuous population. The main reason is that the distribution of the order statistics involves the powers of capital F and also the powers of 1 minus capital F. And therefore, for a typical distribution say normal distribution etcetera these expressions will be interactable that means, we cannot evaluate them in the closed form. Therefore, pattern procedures have been developed for which we can at least obtain approximations or we can obtain bounds. So, first I will discuss the method of lower or the upper bounds for the expected values. So, first assumption is that let us make assumption that F is strictly increasing and second is that second moment exists. So, in general or we can say sigma square is finite that means, the variance of say x i that exists under these assumptions this expressions will be obtained. So, let us consider say for example, distribution of the largest. Now, we have derived the distribution of the largest as n times F of x to the power n minus 1 f x and multiplied by x here. Now, we substitute say u is equal to f x. So, of course, d u is equal to f x d x then this is becoming equal to integral from 0 to 1 and place of x we will have f inverse. This is the reason why we make the assumption that f is strictly increasing because then I can write down the inverse function in a unique question. Then this is becoming n times u to the power n minus 1 d u. Now, this terms we make some adjustment here we write it as 0 to 1 f inverse u minus mu. Now, what is mu? Mu we take to be mean of x i.  Now, this is a cross product term on this I apply Cauchy Schwarz inequality and also let us look at what are these terms. Let us check each of them separately.  So, this is nothing but mu itself. Similarly, the integral 0 to 1 n u to the power n minus 1 that is simply becoming mu by n then we apply Cauchy Schwarz inequality on the first integral. That means, on this term I apply the Cauchy Schwarz inequality.  Once again what are these terms?   So, that is minus 1 that is equal to n minus 1 whole square divided by 2 n minus 1. So, let me substitute all the values here. So, we get using the above computations we get we started with the term expectation of x n. So, expectation of x n is less than or equal to sigma into n minus 1 divided by root 2 n minus 1 and then what are the other terms that we are getting here this term is giving me mu this is giving me mu this is mu. So, this is getting cancelled out. So, I get only mu here. So, you can say this is a bound here to find bound on expectation of x 1 we replace x i by minus x i. So, then we get expectation of x 1 greater than or equal to mu minus sigma n minus 1 by root 2 n minus 1. So, basically you can see that moments of the order statistics lie between mu minus sigma n minus 1 by root 2 n minus 1 to mu plus sigma into n minus 1 by root 2 n minus 1. Let us take say some special case for example, I take n is equal to say 5 if I take n is equal to 5 then what value I will get this sigma n minus 1 that is becoming 4 and this will become 3. So, 4 by 3 that means we are getting expectation of x 1 is greater than or equal to mu minus 4 sigma by 3 less than or equal to mu plus 4 sigma by 3. So, it is helpful in that sense for example, we know expectation of each x i is mu. So, now I want to talk about expectation of x n. So, the upper bound that is attained when I have a sample of size 5 is mu plus 4 by 3 times the standard deviation of the random variable and similarly the lower bound will be mu minus 4 by 3 times of the standard deviation.  So, this is giving us the similar bound in the case of the order statistics from any distribution. Then one question may arise for example, this derivation that I have done is through Cauchy Schwarz inequality. Now we know that in the Cauchy Schwarz inequality the equality is attained if the two functions f and g are basically linearly related. Now if we apply that condition then certainly equality must be attained. So, we can actually show that this bounds are sharp that is there exists a distribution for which these bounds actually that example is given here. So, let me mention that thing here that is if I consider f x is equal to 1 by n minus 1 b by n 1 plus b x by n to the power 2 minus n by n minus 1, where x is from root 2 n minus 1 by n minus 1 to root 2 n minus 1. If I consider this density of course, it is 0 outside this range for this density both the bounds are attained which can be easily checked I am not giving the calculations here. Actually if we consider this the form of the CDF is also in a closed form and therefore, all the calculations can be easily done here. Now if the distribution is symmetric about 0 then that means mu is 0 in that case there is a further improvement over the bound let me give it here. In case f is symmetric 0 then let us consider generally if it is symmetric then we have this property that f of minus x is equal to 1 minus f of x and also a small f of x is equal to f of minus x and you will have mu is equal to 0 that means variance will be equal to expectation of x square. Now in this case let us consider say expectation of x n so that is equal to minus infinity to infinity n times f of x to the power n minus 1 f x dx. Now this is multiplied by x here I split it into the two regions minus infinity to 0 plus 0 to infinity. In the first one you put say y is equal to minus x then this is becoming 0 to infinity then x is becoming minus y then you get n times f of minus y to the power n minus 1 f of minus y dy. Now using this property of symmetry here this is becoming equal to minus 0 to infinity y n 1 minus f y to the power n minus 1 f of y dy. So again you can put y is equal to x so I can now consider this integral is 0 to infinity this integral is 0 to infinity this is with a minus sign and here I have n y that is n x here and f x so that is common here.  Now you can again put as before u is equal to f y if we do that then this is simply becoming equal to n times half to 1 why half to 1 because f inverse 0 since it is symmetric about 0 then f of 0 is equal to half so f inverse 0 is equal to f inverse 0 will become equal to half.  Again you see this is interesting here this is coming as a product of two terms. So I can apply Cauchy-Swar's inequality we can use Cauchy-Swar's.  So it is a matter of calculations here this is actually becoming x square fx dx from 0 to infinity. So since I have assumed that the mean is 0 and it is a symmetric function. So it is actually equal to minus infinity to infinity half of that. So this is basically equal to sigma square by 2 this can also be easily evaluated. So I just write down the values here it is becoming equal to n sigma by root 2 because power half is coming here and in the second part it is coming 1 by 2 n minus 1 minus n minus 1 factorial square divided by 2 n minus 1 factorial whole to the power half. Of course you can further simplify it as equal to n by root 2 n minus 1 into root 2 sigma 1 minus 1 by 2 n minus 1 c n minus 1 to the power half. If you compare with the bound that we obtained here it was sigma n minus 1 by root 2 n minus 1 a plus mu. So this mu is actually becoming equal to 0 here. Here you can see that sigma this divided by root 2 n minus 1 is coming here but this is n minus 1 here that is becoming n here and here you are getting root 2. So this bound is much smaller that means it is a sharper bound if we are having additional information that the distribution is symmetric about 0. So, here what you can see here that we have made use of the Cauchy-Swarzen equality for the evaluation. Then of course one may question that why did I not consider R-th here. If you consider the R-th one then there is a difficulty here. See in the R-th one two terms will be coming here. So here it is easy because if I do it for one of them then I am able to convert it into x. But if I do the second one then it is becoming 1 minus x and I would not be able to evaluate there. I mean it will become much more complicated. Then the second is the asymptotics here. So let me talk about that. So we look at asymptotic expressions for mean and variance of order statistic. So let me talk about that. So first I develop a general formula. So let us consider say let z be a random variable with expectation of z given to be say mu and let g be any measurable function.  I am applying Taylor's theorem here Taylor's expansion. So I am assuming that g is a nice function that means it is differentiable many times. At least two times we are writing down the term here. So if I take expectations on both the sides taking expectations on both sides I get expectation of g z that is equal to g mu. Now in the second one if I take expectation this is simply vanishing and then I get here expectation of z minus mu square. So I have assumed here expectation of this. So this is becoming variance here. So g 2 mu by 2 factorial sigma square and so on. So if I consider say g z minus expectation of g z then this first term will get cancelled out.  There are other terms also we can write it as a sigma g i mu by i factorial z minus mu to the power i minus basically mu i that is the mu i is the ith central moment of z. If I take this then I get this term here and then this is from i is equal to 3 to infinity square of this. So if I expand this I will get g 1 mu square z minus mu square then next term will give me minus 2 times. See this sigma square term is there. So if I consider this expansion that is sigma square the cross product term with this I will get 2 times g 1 mu z minus mu then g 2 mu by 2 factorial z minus mu by and sigma square and then certainly all the terms that I will be obtaining from this that is when I square it then I will get the cross product with this one. So let me just put that general form here minus 2 g 1 mu z minus mu sigma g i mu by i factorial z minus mu square into mu i i is equal to 3 to infinity all these terms will be coming there then I will get square of this term that is plus g 2 mu by 2 factorial square and then I will get z minus because I have already taken the cross product of this separately. So I will get a term which is giving me sigma square. So sigma to the power 4 basically and then cross product of this with this itself. So I will get sigma to the power 4 minus twice sigma square z minus mu square. So basically I am just arranging in a you can say that I am arranging the terms in a particular way then of course then there will be terms with you square at this then that will give me z minus mu to the power 4. Here the powers are starting from cube. So when I square it then in the cross product with this itself I will get 3, 4 and so on. So all those terms I write as h of z. So what I have done I have written the terms only up to square order of z minus mu. Now that was the reason that I assumed up to the variance only because I am not going beyond that. This approximation is dependent upon this choice here. Now let us consider here variance of g z. That means if I take expectation here that will give me the variance of g z it is equal to expectation of these terms. If I take expectation here this will give me sigma square. Here this term will simply vanish. This term will simply vanish. This term will again give me sigma square. So sigma to the power 4 minus 2 sigma to the power 4 plus expectation of h z. So this we write as g 1 mu square sigma square minus 0 minus 0 plus g 2 mu square by 4 minus sigma to the power 4 plus expectation of h z. So if we ignore these terms ignoring expectation of h z variance of g z is approximately equal to g 1 mu square sigma square minus sigma to the power 4 by 4 g 2 mu square. This gives an approximate expression for the variance of any function of a random variable in terms of mu and sigma square. So that means the first and second moment must be of a known form. Now what we do we make use of the order statistics here that is since if I am considering order statistics then f of that is becoming uniform. So if we use that then let us see. So this x r is the r th order statistics. So if I consider f function f function is giving me u r that is the r th order statistics from uniform 0 1. Why I am taking this because I know the mean etcetera of this. So actually I am putting z is equal to u r that is basically we are having expectation of u r is equal to r by n plus 1 and variance of u r is also known that is r into n minus r plus 1 by n plus 1 square into n plus 2. So we will actually so this mu and sigma square that is this is mu and this is sigma square and f inverse if I put here that is g function I am taking to be choose g is equal to f inverse. So if we do that and z is equal to u r in this formula let me call it 1 then what I am getting I am getting here well let us consider the first expression in one and this expression that I wrote here I can call this as 1 and this as 2 say. So in 1 and 2 so what I will get here that expectation of x r is asymptotically equivalent to f inverse r by n plus 1.  Actually this term is coming from the derivative of f inverse there because let me show the calculation here for the derivative. See if I am considering say d of f inverse x by d x then that is actually becoming 1 by f f inverse x and if I consider say for example if I write y is equal to f inverse x then what is the value of say d 2 y by d x square. So this is actually d y by d x. So if I consider second derivative I will get minus f prime y by f y d y by d x square.   So this is actually a first approximation I can consider two terms also that is if I take this one then it will become second approximation will be 1 by f f inverse r by n plus 1 square r into n minus r plus 1 divided by n plus 1 square into n plus 2 and second term will give me 1 by 4 that is this one sigma to the power 4.  So this is a second approximation here. So if the form of capital F is known you can have the expressions for the order statistics and the amount of the error in these approximations is not much one some calculations have been done for various values of n and r for a specific distributions and then one can check that how much error is there. And these approximations are quite satisfactory especially if I consider the second order approximation. So this approximation made use of the fact that Taylor expansion is possible and second thing is that we assume of course that assumption is not a very astringent assumption because what we are having is that f function I am assuming to be strictly given. So that means basically I am taking it to be a nice function and if that is so I am I am assuming the higher order moments to be negligible and in the sense that we are dividing by higher powers of n. So the deviation will be much less because as you can see here itself in the denominators we are getting the term like n plus 1 to the power 4 n plus 2 square. So if I take further then this terms will be very very high and therefore they become negligible. So it is not a very astringent or you can say bad assumption here as such. Next thing is that one can talk about the asymptotic distributions also. Next we derive asymptotic distributions of Xr that is rth order statistics. Now here there can be two cases one is that only n tends to infinity r remains fixed. So that means for example I am finding out the asymptotic distribution of the minimum the maximum etcetera. So that means the position is fixed but in the second can be that the position can also vary that means I take say r tending to infinity n tending to infinity such that r by n tends to a fixed value. So I will consider these two cases case one r is fixed and n is tending to infinity. So let us firstly consider the case of the order statistics from the uniform distribution. So I am having say u 1, u 2, u n from uniform 0, 1.  Here you take w to be say n times ur then what is the distribution of w it will become n factorial divided by r minus 1 factorial n minus r factorial then this is becoming w by n to the power r minus 1 1 minus w by n to the power n minus r and you will get 1 by n extra term here w is between 0 to n. Let us look at the cumulative distribution function of w that is f that is becoming equal to integral 0 to w and all these coefficients will be coming there. You can actually consider say say this is becoming basically 1 by n to the power r minus 1 factorial and this is w by n to the power n minus r. So if I integrate I will get let me write it here. So all these coefficients will be there then I have t to the power r minus 1 1 minus t by n to the power r minus sorry n minus r dt and other coefficients will be there which I have not written here. If I take the limit of this as n tends to infinity then what I get here? See this term will go to e to the power minus t here and first thing is that the limit will exist and this will go to e to the power minus t because this term will go to 0 t by n tending to. So now if I take the limit of this coefficient here you can check what are the terms that are coming here. You are actually getting n to the power r in the denominator and here you are having n into n minus 1 into up to n minus r plus 1 divided by n to the that means basically there are total r terms here. In the denominator you are getting n to the power r. So each of the terms will be adjusted like you have n by n, n minus 1 by n, n minus 2 by n up to n minus r plus 1 by n. Each of these terms as n tends to infinity will converge to 1. So if I take the limit here this is converging to exactly a term of the type 0 to w 1 by r minus 1 factorial e to the power minus t, t to the power r minus 1 dt. So this is very instructive here. You look at this, this is nothing but the CDF of a gamma distribution that means we are saying asymptotic distribution of so as n tends to infinity the distribution of n times u r converges to gamma r 1, scale parameter 1 here. So that is one result that we are able to obtain. Now let us consider CDF of x r. So if we consider the CDF of x r what is happening here? f of x r at some point say x that is equal to probability of x r less than or equal to x which we can write as f of x r less than or equal to f x. So this is equal to and we can multiply by n also. So this is nothing but n u r less than or equal to n of f x. Now we are showing that this is converging to 1 by gamma r integral 0 to n f x t to the power r minus 1 e to the power minus t dt. So this is very interesting actually we are able to obtain the general form of the limiting CDF of rth order statistics as the sample size tends to infinity. And if we can consider the derivative here then limit of that also can be obtained as 1 by gamma r n f x to the power r minus 1 e to the power minus n f x n f x because I am just applying the Lybden's rule here. So this is derivative of this is becoming n f x and here n f x to the power r minus 1 e to the power minus n f x. So we are able to obtain the general form of the limiting probability density function of the rth order statistics here. The second part is in this one you can see that we have applied the condition that r is fixed but n is tending to infinity. Now the second can be that I can take both an r and n to be tending to infinity such that r by n tends to a fixed number. Actually what is the difference here? If r is fixed that means I am finding say suppose for second one or third one etcetera. But if I take r also tending to infinity that means I am fixing the position for example it could be middle like median or a quantile. So there is a difference in the treatment here. We may also see what happens to this thing for example if I look at say limiting density for the first one then what happens then r is equal to 1 here so this term will go away, this term will go away. You get simply e to the power minus n f x n times f x d a. So this is a very very interesting thing that asymptotic distribution for a general form for the minimum can be obtained which is of course you can say it is an exponential form and that is why in the negative exponential distribution basically you are getting n times that density was repeated there. Let us consider case 2 r tends to infinity n tends to infinity such that r by n tends to p.  So the density of u r is known so let us write that actually I already considered this density here.   Another thing is the range here u is between 0 to 1. So that will give me the range of v from minus mu by sigma to 1 minus mu by sigma that is minus mu by sigma less than or equal to v less than or equal to 1 minus mu by sigma here. So let us write the terms in a slightly adjusted fashion. So n factorial sigma r minus 1 factorial n minus r factorial this mu I will take out from here.  This term I further express as n factorial.  The c n r coefficient is actually all these terms which are written there. So I am just omitting that here.  If I take here r tending to infinity n tending to infinity such that r by tends to p then this can be shown to be convergent to. So you can actually use some Stirling's approximation. If you remember Stirling's approximation that is n factorial is approximated by root 2 pi e to the power minus n n to the power n plus half. If we use this approximation then this can be written as root 2 pi e to the power minus n n to the power n plus half divided by since I am taking r also tending to infinity.   So this cancels out e to the power minus n cancels out then e to the power minus r and e to the power plus r also cancels out. So you can actually show I mean one can basically obtain the limit of this. This is actually converging to 1 by root 2 pi. Basically what you will get 1 by root 2 pi term here and then all other terms can be adjusted easily 1 plus 1 by n minus r to the power n minus r then you have 1 plus 1 by n minus r to the power half that is coming by division here because see I am getting n minus r n plus 1 minus r here. So this I divide here. So I take the equal power which are coming that can be divided here and similarly in this one. So this I will get as 1 plus 1 by n to the power n and I will get 1 plus 2 by n to the power half. So now if I take the limit this is simply 1 by root 2 pi then this will give me e in the denominator I will get e and this will give me 1, this will give me 1. So this I will get as simply 1 by root 2 pi. So this coefficient C nr this converges to this as n tends to infinity r tends to infinity such that r by n tends to p. Of course r by n has not played a role here but because all the terms are not coming in that particular fashion. Now let us look at this part.  If I consider this so we can consider expansion of this type of forms log of 1 plus x by x plus 2 that is equal to x by x plus 2 minus 1 by 2 x by x plus 2 square and so on 1 by 3 x by x plus 2 mu. This type of expansion will be valid if I consider minus 1 less than x by x plus 2 less than 1 that means x greater than minus 1. Similarly I can consider log of 1 minus x plus that is becoming minus x by x plus 2 minus 1 by 2 x by x plus 2 square minus 1 by 3 x by x plus 2 cube and so on. So if I take the difference that means let me call it a and b then if I do a minus b then I will get this as log of 1 plus x equal to twice x by x plus 2 plus 1 by 3 x by x plus 2 cube 1 by 5 x by x plus 2 to the power 5 etcetera. So for expansion of this I am unable to use directly that this is between minus 1 and 1 therefore I am using another form here. This expansion will be valid provided x is greater than minus 1 but that is true here. Here this sigma v by mu is greater than minus 1 and similarly this one will also be. So if we consider this then I get log of 1 plus sigma v by mu is equal to 2 times sigma v by mu divided by this is of course slightly cumbersome expression but still one can write it in the closed form. So this cube and so on. In a similar way I can consider in a similar way log of 1 minus sigma v divided by 1 minus mu. So that is 2 times sigma v with a minus sign here twice 1 minus mu minus sigma v plus 1 by 3 cube and so on all this type of terms will become.  Now if I define something like c 1 is equal to sigma by mu that is equal to root r into n minus r plus 1 divided by n plus 1 square into n plus 2 n plus 1 by r then this is actually n minus r plus 1 divided by r into n plus 2 then if I use r by n is equal to approximately p then it is equivalent to 1 minus p divided by n p. In a similar way I define another term sigma 2 that is sigma by 1 minus mu that is root r by n minus r plus 1 into n plus 2. So that is approximately p divided by n into 1 minus p as r tends to infinity n tends to infinity r by n tends to p. And in terms of this c 1 and c 2 of course r minus 1 is also equivalent to n p r by n is r is equivalent to n p etcetera all these terms will be using. So let us substitute here. So what I get t is there are some more terms that will be appearing here let me write it here.   Now this c 1 and c 2 I defined here and I obtain their asymptotic expressions here. There will be other terms coming there for example r minus 1 c 1 to the power 2 m plus 1 then this will be approximately n p by 1 minus p by n p to the power m plus half which we can of course write as say k 1 n to the power minus m plus half of course that will go to 0 as n tends to infinity.  Similarly if I consider say 2 plus c 1 v that will go to 2 2 minus c 2 if I consider that will also go to 2.  So, easily you can see these terms get cancelled out and this term itself will get cancelled out with this term and we are left with actually minus v square. So, what we are getting is that t converges to minus v square by 2 as n tends to infinity r tends to infinity and r by n tends to p. So, what we have proved is that if I consider the limiting distribution of limiting pdf of v, v was u r minus mu by sigma as r by tending to infinity n tending to infinity and r by n tending to p as 1 by root 2 pi e to the power minus v square by 2 that is u r minus mu by sigma converges to normal 0 1 that is a very very significant result and we can say that asymptotic distribution of u r that is r th order statistics is normal with mean mu that is r by n plus 1 and variance is sigma square that is r into n minus r plus 1 divided by n plus 1 square into n plus 2. This is the asymptotic distribution of this which of course you can say as p and this is r by n is approximately p and in the second part you can write it as 1 minus p divided by n that is approximately p into 1 minus p by n. So, you can think of this as actually binomial type of terms here mean is n p and the variance is n p into 1 minus p etcetera. Now, if I use the inverse function here if I use the inverse function here then this is becoming f inverse p that means it is the pth quantile coming here. So, let me write it here it in the form of a theorem. So, basically we are able to obtain the asymptotic distribution of u r as the normal distribution here and therefore, if I use the inverse function which I will be giving in the tomorrows in the next lecture the asymptotic distribution of the r th order statistics under these assumptions is obtained as a normal distribution. So, you have two cases one is when r is tending to infinity n is tending to infinity and r is fixed in that case you are getting related to gamma function and here you are getting related to the normal distribution. I will be using this for obtaining confidence intervals for the population quantiles as you I have mentioned that in the nonparametric situation rather than considering the means and the variance etcetera we discuss the positional point that is the median the quartiles the quantiles the percentiles etcetera. So, I will be doing it in the next class.


Hello friends, let's work out the following problem. It says using differentials find the approximate value of the following up to 3 places of the decimal. So let's now move on to the solution and first of all define y as a function of x and let's take it to be x to the power 1 by 4 and let x be 16. Here we choose x in such a way so that we can easily find out its fourth root and we know that we can very easily find out the fourth root of 16 that is 2. So now we take delta x as minus 1 as we need to have x plus delta x as 15 so this would be 16 minus 1 that is 15. Now we know that delta y is equal to f of x plus delta x minus fx so this is x plus delta x to the power 1 by 4 minus x to the power 1 by 4. Now x plus delta x to the power 1 by 4 is 15 to the power 1 by 4 and x to the power 1 by 4 is 16 to the power 1 by 4. So this implies 15 to the power 1 by 4 is equal to delta y plus 16 to the power 1 by 4. 16 can be written as 2 to the power 4 and its power is 1 by 4 so this is equal to delta y plus 2. Now we know that delta y is approximately equal to dy and dy is equal to dy by dx into delta x so delta y is equal to dy by dx into delta x. Now y is x to the power 1 by 4 so dy by dx will be 1 by 4 into x to the power 1 by 4 minus 1 that is minus 3 by 4 into delta x and delta x here is minus 1 so this is equal to 1 by 4 into x to the power 3 by 4 into minus 1. Now again substitute the value of x and x is 16 which can be written as 2 to the power 4 and its power is 3 by 4 so now we have 2 to the power 3 into 4 that is 8 into 4 that is 32 into minus 1 so this is equal to minus 1 upon 32 so this is delta y now 15 to the power 1 by 4 is delta y plus 2 so 15 to the power 1 by 4 is equal to minus 1 upon 32 plus 2 that is this is equal to 63 upon 32 that is equal to 1.96875 hence the answer is 1.96875 so this completes the question and the session bye for now take care have a good day


I'm sure that today in Washington DC there are a lot of great things to do, but I am not doing any of them. I'm sick. Right now I'm going to call my boss and tell her I cannot come into work. Ms. Weaver? Hi. I can't come to work today. Why not? What is wrong? Well, yesterday I felt fine. In the morning I painted for hours. In the afternoon I cut wood. Then I built a fire. Anna, what do you mean? Why can't you come to work today? I do not feel well. I think I'm sick. I'm sorry to hear that.  I had the flu. What did you do? I slept a lot and I drank a lot of water. Do you have a doctor? Yes, I do. You should call your doctor and get lots of rest. Thanks, Ms. Weaver. I'll call right now, calling my doctor. I do not feel well. I think I'm sick.  I had the flu. Now, where does this thing go? This is Dr. Bennett. How can I help you? Hello, Dr. Bennett. This is Anna. Oh, hi Anna. How can I help you? I think I'm sick. Let me ask you a couple of questions. Do you have a sore throat? Yes, I have a sore throat. Do you have a cough? Yes, I have a cough. When did you start feeling sick? This morning. Yesterday, I felt great. In the morning, I painted for hours. In the afternoon, I cut wood. Excuse me, Anna. But I don't need to know all that. Do you have a fever? My thermometer says 125 degrees. What? Yeah, that's not right. Oh, wait. The thermometer was in my hot cup of coffee. Please, take it again, Anna. The thermometer says 100.5 degrees. 100.5 degrees is not too high. I want you to drink lots of water. That is what my boss said to do. Um, Dr. Bennett, when can I go to work? Don't go to work for a couple of days. Yes!  Call me back in a couple of days. When did you start feeling sick? Well, you heard the doctor. No work for a couple of days. I need water, sleep, and lots of movies. Well, the doctor didn't say anything about movies, but it can't hurt. Until next time.


Might as well do a little video. So for an impeller change on an old Yanmar 15 like this one QM I think this one is if I remember correctly the the pump sits like sits like this on these bolts And to get to the impeller you got to take the pump off to get to the back there to open it up So you know you don't even get an advantage from having a speed seal plate on it because you've got to take the pump off Anyway, just to get to the back Obviously on modern designs. They've Reversed it so that you can you can open the the seal without taking the pump off, but you know 1980 90s late 70s this engine so Let's continue and as I suspected the impeller is fine So it's just the inlet which is a bit crusted up, which is why it doesn't quite get enough water all the time But I think I might change this impeller anyway I'll just check. I mean I've got plenty of spares. I'm just not quite sure if I've got the right one. Let's have a look Yeah, I've got four spare Impellers and they're all the right ones But I really don't think I need to change this because it's in perfect condition. There's no cracking on any of the arms I'm gonna leave it But you know at least we've had a look Think I've got a seal to go around there. Let me just check All cleaned up with some wire wool got a new paper gasket for it. So now let's try and get it on without ripping the gasket There we go. All done.  I just got to fit it back on the engine Use the lugs on the engine to mount the pump so that when you attach the pipe It's in the right orientation and you don't end up because if you if you attach the pipe or the pumps not on the engine You might have it twisted, but you don't want so very easy Just put it in the right place first then attach the two pipes then take it off Put the belt round and then put it back on Now before I put the pump back on I'm going to take this opportunity where I've got a bit better access To just take the strainer out of there check that it's clean And maybe poke something down and see if I can de-crust the inlet pipe a little bit So this is the strainer which goes inside that body there Can you see? There we go. Yeah So this strainer goes inside that body there So all the water that comes up comes up the inside of this and then into the engine and You know, that's not bad. There's hardly anything in there. So I'll give it a quick wash and a rinse And then I'll poke something down the floor So it's all back together Pump is back on belt tightened Now I do have a problem. This is a pencil anode into the engine There's one on the back as well, and I checked them two years ago And they were fine But I obviously tightened it up too much because I can't get it off And I tried some percussive engineering, but that did not work either I don't want to bash it too hard So I'm going to wait Until I get back to Valencia having run the engine for some time getting in It'll be hot then And I'll try and take them off when the engine's hot. I'm also going to do the oil change then as well But you know 19 this stop making these engines in 1980. So it's at least What's that for 30? It's very old