Second time to Portland and I paid Sam not to mention any of the shenanigans that we may or may not have done You know in the past But these are always telling somebody at lunch today. These are always hard because how do you tell like? There's several tracks here a user track business track developer track, and so it's already always hard But this has kind of been resonating Simmering I think in me as like Sam said earlier this year We we were acquired by liquid web, so the business I ran for ten years sold and just it was kind of a nostalgic time I'm just thinking back. Okay. What? How how the heck did I end up here? I'm very grateful and fortunate to be have ridden the WordPress training for a long time and So it's kind of just thinking back and it just felt like it's obvious to my wife She was here. She should actually give the talk. She doesn't bet. She knows me even better, but So I wanted to share what I think is my what I I shouldn't say I think I know is my secret weapon for success So I'm gonna take you back 12 years ago I was sitting in an office in a church in Oklahoma City, and that was my job I was a communication instructor So I'm telling you these things because I want to contrast some stuff And then I want to share my secret my dirty little secret so 12 years ago I was basically like a glorified copier guy like I was doing the The bulletins for the Wednesday and the Sunday church services and things like that and I was sitting in a borrowed desk My my office had two like the weird doors, you know that only I could I locked it of course There's one behind me, but the transition was really interesting And I had really only managed the part-time person up to that to that point And not for that job job previously and the guy that was in the job That my previous job that I've managed basically was a grad student that could have done the job that basically trained me So to say I've managed the part-time person was probably a little bit of a stretch, too so then Then 2008 like Sam said By the way when I was sitting in that office and everything at night I was blogging with WordPress and I started with blogger quickly found this thing called WordPress and Put myself out there my ideas to be potentially criticized But also seemed by people and for a long time a brag that my one subscriber was my mom and Eventually that built into things and then I put a free theme out Because I wanted to learn web design. I'm not a developer by the way I don't try to even pose for one on TV But so in 2008 pitch to my two partners the idea for what would be I themes but you know this so so the ten-year journey from 2008 to 2018 culminating with being acquired by liquid web like Sam said I'm still running I'm still running our team within a bigger 500 person hosting company So my title has changed a little bit. Huh? Oh, I'm sorry about somebody said something. I know I need hearing aids So anyway, um, but you know just looking over that ten-year period of time where today we have about 20 people We have seven people in seven US states four countries and two comments and I like somehow I went from this little copier guy glorified a copy. I did a lot more. It does stop publishing But I made copies of those things Then to the incredible ride that I'm thankful we had at I themes where we built great products Talk to some customers at lunch actually and it was a fun time but when I look back I go, how did I get from here to there and by the way, I'm I'm this kid from a town called Lone Grove, Oklahoma. It's in southern Oklahoma There's 3,000 people in the town and there is one sonic like there's a sonic We have a sonic drive-in at long good And one stoplight so how do you know I kind of picture myself sometimes going how did I do all this? So I want to share with you my secret weapon Okay, of when I look back I go this way There's a lot of ingredients that went into success collaboration of a talented talented team Really good relationships with people and things like that Well, I think how did I go from this to start managing people to building what I think is a really good culture at art At I themes that people want to work at I themes Here it is now This is the grand finale and I told somebody this last night and he kind of went. Oh, that's what you're gonna You know and he goes well now I'm gonna have to actually come and listen to your talk I said it's my probably unpack it a little bit better tomorrow, but anyway, I read But I don't just read so I've read Not just going back 12 years, but my entire life I remember going to the Chickasaw Library in Ardmore, which is the bigger town You know, there's a small town in the bigger town and just grazing the aisles of the library So I was like this this is like all this knowledge and everything put in these cool little forms called books but I've always read very voraciously and but I really I've read strategically so that's what I want to unpack for you how I've read How I've leveled up and done things that honestly I wasn't trained to do but I've went Problem-by-problem situation by situation gap by gap every gap that I had I'd go acquire find the right book and Read it and I want to change. I want to share that with you exactly. So Reading has definitely reading in a different way reading strategically. That's the way I read Has changed my life. It's made me money You know when we were thinking about the potential deal from hiring our first person I went and found books that would would help me educate me and Become a more confident person or creative person innovative. What I'm trying to tell you is I'm not that smart to do all this stuff I had to go find books and people that would help me do But also to become a better dad better father Husband and I think human so okay last couple months this has kind of been simmering so I went back to Amazon and Looked and this is if my wife sees the statistics. She's gonna really be mad at me But like I realized just from when I could get my Kindle purchases On Amazon it must have came out in like 2018 or 2011 or whatever last eight years I was like 800 books. Holy cow. Now. Let me give you a caveat. I've not read Cover-to-cover all those books But what's so interesting is the trail when I started looking through this list I had to copy and paste into a spreadsheet and try to look through through them and I go I could see seasons of times in my life Where I bought this collection of book just on the purchase. It's kind of interesting If you do the math which my wife has recently this year It's a small fortune in books and but The beauty is I carried around with me like all of those books I carried around have access on my phone I'm gonna talk to you about that in just a second So books are magic now you guys are probably readers you're here your learners and things like that But I think books are magic because in a $20 little package roughly $20 little package someone Who has spent years and years and years experience and expertise all that has been forced to Put all of that in a very clear succinct manner, so I think they're I think they're pretty magic and then I get to carry it around in my pocket now But my library my library has been my board of directors My council of elders my tutors and teachers all these years now I've had a lot of help in person help but dead trees are a big part of my success so I think Reading and reading this specific way has definitely helped me and I'm gonna share some examples of how specifically When there was moments of the gaps realizing like I'd not really managed any Person and then all of a sudden the first year we had four people How are those things really helped me but I honestly believe Best investments and by the way so thinking about next chapter in my life. What am I doing? I'm reading I actually did pick up a print copy of a book on purpose and meaning from HBR at the at the Airport because I didn't want to drain my iPhone So I mean just thinking about next steps. I'm still doing that best investment best investments ever So I read to get an edge I read now These are my dirty little singers by the way because I I have met people that can out hustle me way smarter than me I actually have really good original ideas and I knew I had to find an edge somewhere So to get ahead stay ahead to level up mind the gaps every every big major event around I themes I was looking at in books and then taking those Ideas and inspiration to use in our business and in my personal life so this is the key read for inspiration and ideas but They're the cheat codes. So I started thinking through like all the books I read or have read Strategically not covered by the way. These are what these are the things that I've gotten from them I mean courage is on there So reading stories of how someone else did something but the templates perspectives formulas models processes I have the surgically extracted those from books over the years You know when we were thinking about new products Strategies for being a very small team and outnumbered and Outmoneyed whatever that phrase would be having more money than what we did I went to books and try to find okay Is there a case study for some you know David versus Goliath kind of thing is there some model of thinking strategically that You know in my limited creativity. So these are my cheat codes books are my cheat codes I'm gonna give you some examples. So 2008 By the end of the year we had four people and I had never like I never managed anybody so these two books I mean and the third that I'll mention in just a second are how really the cheat codes for how I had approached Our building our team recruiting people maintaining a fantastic culture that people want to be there and then also do their best work So 12 elements of great managers by the way these two books I'm currently there's two people on our team on the kind of coaching and I'm having them go through these books because they were so Instrumental I was looking back because I haven't reread those books in a while and I was looking at the table of contents and go Yep, this is basically the blueprint of everything we've done one of the chapters in the great managers book Which by the way is based on Gallup research Was have a best friend at work. I was like duh Man the happiest times I've had is when I've had really good friends. So, you know, we did Not everybody on the team is best friends Maybe not everybody likes each other at every moment, but we at least enjoy each other and so I'll give you an example Elise is one of our awesome Team members. She's been with me for I think six years now. I've done great. We're looking for a new Person a couple years ago. She goes well my best friend Sarah You know Let's talk to Sarah and Sarah has an MBA and now she's doing a great role But they they literally our best friends and now work together, but I took some of those elements of these things another thing was I think second chapter is Make sure this is obvious stuff, right, but I think It's good stuff for me But it was if make sure your team has the right tools and equipment like duh I mean, how can you not do your work? But I found out one of our developers for like three months when he first started didn't have an extra longer I'll get you a monitor. I want to make sure you have all the right tools. Anyway, that stuff came from here leadership challenges One is model the way Inspired to share vision as I've been kind of coaching and walking through some of our team members of that I'm going this is this is just copy and paste what I've been doing for ten years So that one's good. How to empower others. Have you anybody read this book? No, okay. Well, I'm sure it's something new. Okay. It's called drive by Daniel Pink Basically the premise is this autonomy mastery and purpose. That's what we want, right? Think about your job You want autonomy you want the freedom to like do your best to pick your you know to pick the things that you do Do well mastery you want to master what you're doing and then purpose you wanted to connect to something Helping people those three things are the things that we just do have done it. I think it's in it. I took the cheat code, right? I had to go now How do we do that because then we gave gave people way too much autonomy and maybe some took advantage of it Okay, well autonomy with guardrails, you know on it. So anyway The culture and the team and the great things that we've done over 10 years has been shaped by those three books Okay, so how to how to think better or that's okay, you know, sometimes the machine up here doesn't work the best That's a fantastic book how to think through things. I use that when we were trying to plot big strategic moves Think through, you know new initiatives stay competitive in the game This is a great one how to be okay say no basically if you're like me you're probably like You know not a lot of boundaries Fantastic book it gave me the freedom and confidence to say no to people and and still feel like I was a good person Okay, so here's another one Navigating mid-life. I'm 42 now, but a couple years ago. I was like It wasn't necessarily a crisis, but it was a brinne brown calls it done and then an unraveling and I was like Yep, I was unraveling. So you look at my purchase list and you go okay I found these two books and they were incredible help me have some I don't know I can't hire those people You know what I mean? I can't get in front of them, but I can go take their wisdom to still down into a book and do that so I Said my purchase history is like a trail of my life and it really has just going back like in 2010 or whatever from that Just a Kindle side of things I was like I know exactly what I was going through during these periods of times because they were I was just going book by book Trying to navigate with myself through these periods of time. So okay, let me give you Here's my keys. This is where I want to drill down next to be really as practical as I can in X amount of time Okay, so the first is some of you gonna fight me on this But I had to ditch, you know, it's been about eight years, but I finally ditched my whole need of all I love the filip paper Fanning the book in front of my face and send it a coffee shop. I mean like I read, you know I Finally had to get over that little thing now every now and then it's cool to have like the Harvard Business Review, but anyway The Kindle is the best tool ever for reading like this if you don't and I'm not talking by the way the Kindle is not Just a physical device you can buy on Amazon. It is basically the Kindle was a reading platform and it has a ways to go I wish Amazon would call me and I would help with some stuff, but like But the Kindle you've got reenacts where like I said you can take your entire library here on your phone You know we used to go on vacation. I take like three books And it's like do you have underwear Corey in your suitcase? I mean it's very heavy with books, but did you forget some of the essentials now? I get to take them with on the book but on my iPhone But I would say if you're really serious if you get serious about this This is the only way to go because you can make highlights you can store it all on your reading platform It's access. It's convenience sufficiency It's cool to read a book and then tab you know tab over the thing or highlight it But when you want to go back and try to find some cool quote that you you want to share with somebody or you're trying To remember something it's kind of hard to like oh man That's at my library and you know my bookshelf of the office and I really need it right now No, I can search those things on the Kindle. So I mean if you really love the print stuff Seth Godin says by the souvenir coffee. So the books that really resonate with me I go by the print book and put it on the shelf. So the cool whenever it comes in my office And can also point one amount to but the Kindle that's the way to do it So I don't read books. I use them and there's some key things here I think that we There's there's a way to approach reading that is casual and fun and entertainment. That's not what I'm talking about here I don't just read books. I use those books as tools for my life So I read for me and it's the if this than that statement. So If I'm in this situation and I'm starting to catalog all my books and go Here's how what it resonates when I say the drip when I tell you about drive the book drive Tonomy mastery purpose kind of thing trying to categorize that by going okay if this situation Then that book and come up with some of those But I think you have to be clear obviously as you're reading strategically You got to get clear on what you're looking for and specifically it's the gaps challenges problems and situations So I approach every book on it like the book. I bought at the airport I was like that's an area a gap that I want to kind of strengthen what I do to have confidence and so In my head I make sure that That book somehow Fills in helps me with confidence Information for action to to figure out one of those things But you got to be clear on what you're looking for and there's still there's sometimes some book There's a book I'll find and I'm like it's a cool book And I'll buy it but it goes in the bookshelf it goes in the Kindle You know, I don't read it instantly But I know at some point I'll probably come back to it. So anyway clear on what you're looking for But if you really just still it down This manner how I read is I read for confidence, you know, somebody said why do people ask advice Ask others for advice. It's because you lack confidence in what you're doing I like confidence in all the areas of those 800 books that I bought And I use those books to have more confidence about what I was doing specifically applied to ideas and inspiration Right ideas for how to attack that problem Inspiration for more creative innovative things that I can do in the business in my life. Okay This is something Everybody gets held up because when I tell people I go well just 800, you know, books on Kindle They're like you read all those No, I don't read all those because I don't insist on reading cover to cover somehow I think maybe in our education Process or system or something that we have to go I have not read the book if I hadn't read all the Acknowledgements and gotten all the way through the appendix to the last period. Boom got it I think that's that's that's okay. That's a different kind of reading So don't insist on reading cover to cover. So I think it's the biggest mistake we make I read like a surgeon. I'm going to dissect To find isolate extract dissect those cheat codes, right? So often in the Kindle, there's a popular highlights thing and that's where Um Hundreds perhaps of people have gone on. This is why the Kindle is the best to date Maybe that changes in the year from there right now I can go into any book and see where people have Read the book. So there it's kind of like, you know, if you did this in college I did you bought the used books. You want the highlighted part you get that with Kindle You're checking me. Did you do it to you? Yeah, of course. Come on Uh only the people that did the highlights want the first one because they're like no, no, no I'm like, no, there's people have highlighted that. I think it's great But Kindle has that so I read for precision extraction on a focused mission Now so when you're looking at a book And and on amazon you guys are familiar with how amazon works most every book has a look inside feature So the table of contents is the map to all the gold all the cheat the cheat codes Now I get really frustrated When I think a book is like going to help me with some gap challenge need problem And I get to the table contents and they're really cute.  So if they try to be cutesy and stuff I get kind of frustrated. I had to solve book I got a book last week and I'm blanking on it emotional agility No, wait, no, it's called 18 minutes And I was like gosh dang it this guy he's trying to be fluffy and everything And I just realized right underneath was the the one I'm looking for in the table of contents. And so now I'm like Ignore the fluffy bunny description and go down to like the right juice But this this is Where everything the map of the gold is now even more extended map is the introduction and usually on Kindle you can You can download the book and read the introduction If they've done their job right and I have been through the commercial book author process before They have been forced To really and I'm talking about nonfiction books here, right? But they have been forced in the introduction to really unpack even further the map of the book So you can actually get really good context For the table of contents in the introduction, but that's I you know, they say don't judge a book by its cover Absolutely judge a book by its table of contents And if you need further proof go into the introduction and if that doesn't sell you it's not worth 20 bucks Often nine times out of ten. It's not worth it if they haven't done their work on the table of contents in the introduction um, so Here's the critical part you can get all the way through here table contents get the right books with the right situations in mind And you can forget Or not forget or just leave off the fact that you're not translating transferring what you're reading into action so Reading strategically the way I've read is I When people go, why are you so compelled to you know, read as much as you do? Because I'm looking for ideas and inspiration to apply in my life like a scientist Like in a lab like the business has been a lab for 10 years in my life. Um How how how do I translate these ideas into specific action? Small little experiments that you test and see how they work and function results that you get It's by asking the question How can I use this tomorrow? Like I'm always usually I'm at night, you know reading and bad or something I'm like, huh, okay. How can I apply that in this situation and book by book? I've done that So you got to have your journal handy. Um, so I use a journal app called day one. I really like it so I'm on my channel on my phone typically And uh, then I'll copy it Copy some quote idea thought and I switch over to my day one app So I can capture those and I think that's good. Well, you can do it however you want But this is the way I happen to do it because I want everything electronic where I can search out Remember some kind of quote Okay, so I've tried to distill the the key ideas Now you know my dirty little secret of success. I'm really not that good. I just read a lot And I find the cheat codes you guys know what the cheat codes are right back to the nintendo days and early gaming days Um, that's all I'm doing. I'm just a small town kid still reading finding buying cheat codes. So go read your way to success um That's me. Thanks questions. Yeah Yeah Like I know I have trouble reading business books at night. Yeah We're you know, we fiction at night and nonfiction in the morning any moment I have free time Any any moment so now I wouldn't try to read because I'm I want to interact with people here, but um You know, I'm on the plane Unless I have a headache or just worn out. I try to find any time Possible for me. So I don't know if I have a specific Um time that works best for me and maybe it's you know person specific That's why I like taking my library on my phone because you're in the you're waiting on a dentist, right? you're in the dentist office And it's redeeming the time. It's making use of the time and so I'm always just Got to find the cheat codes got to find the cheat codes kind of thing. So That's a good question. I hadn't thought about that Well, I mean how much time you spend on on social media that you could be reading Yes, you you the the collective you yes Yeah So what are you doing about your children? Are you sitting here reading to them on real paper books? Yes, yes, because this is a totally different purpose, right? One is we want to be careful of the screen screen kind of stuff, but like We do want them to have that. So yes, they have and this is my wife not me I can't take her head for we got hundreds of books around the house. They read books But I yeah, definitely we So we're starting some transitions. I've got five-year-olds and three-year-olds.  I think you know, I want to transfer that skill to them And at the appropriate time if the Kindle's still the best, I'll be like Read the Kindle Or get the Kindle version. Yes, sir. Do you do audio books? Okay, so this is a great. I think there are different learning styles That's not that's not my particular learning style, but I know a lot of people that love audible I think that's absolutely fantastic I do very specifically for audible when it's more parable But um and it's better for me and that's just the way I'm wired I still think if if I should put this on here If not Kindle and audible or audio is the way you learn then go that route I just think it's harder to capture notes, but that's Do reading strategically how you I think learn I tried to I was take I was doing a commute up to Kansas City when I was in graduate school Or and uh if you familiar with C.S. Lewis So I was listening to C.S. Lewis and dang near drove drove fell asleep and drove off the road It was like no more audio books Definitely not from C.S. Lewis is incredibly dry You need some more in playing the chord. Yeah. Yeah more.  Do you ever recommend a series of books or maybe a snippet of quotes or something for your team that you find helps build Oh, he's in or synergy Uh, well first generally speaking, I'm gonna like a drug dealer With books I push books on everybody I can Um, the first one's free. Yeah, we actually did that We actually did that we uh, we loaded up a physical the heart of the divide We bought a couple of candles and gave them to people By the way, I'm sorry. I'm not engineer pushing but um find a way where somebody else finances your books So I can tell for the last 10 years the business has financed my book empire. Don't tell my partners, but So, okay back to your other question was specific situations for Yeah, do you have like a reading list or something that you recommend to your team that you feel like really kind of Brings it together or is that like kind of There's probably a set of books that I would recommend to anybody and I have recommended to the team One that wasn't on this but it would be on it. I'm gonna finally get my catalog going is uh on riding well That one I would recommend to anybody and have to my team because On riding well on riding well, yeah, it's like in the 25th edition of the anniversary or something like that If you just pop in on riding well, it's there and I have a I have a Kind of book list uh on my personal website. You'll just see and say book note So generally yes, I think recently I've been more specific seeing where they may need to level up or Something like I'm trying to prepare the two team members. We have right now for potential leadership management opportunities so leadership challenge and Great the elements of great managers too. We're going through week by week with each other Does that answer your question? Yeah, it does Does somebody else have a question? Well, it's just more common So my company we have a book club and We'll like take an hour in the morning every month To discuss the book. We've all agreed to read together Usually someone's leading the discussion But we typically don't read like business books. It's actually more fiction Yeah, we've always kind of wanted to read and I guess my thought is That there's some sort of in the process of sort of thinking about what you're reading and being critical the kind of growths of sort of critical thinking skills are You know things we want to level up with everyone in the company Yeah, and so that's kind of like but but it's interesting because I've never even thought to read some of these books together with You know other people at the company necessarily Yeah, when we hired our first Second executive assistant we took uh, Matt my right hand guy took patty through uh, how to be a Bad a for the recording And switch myself. Okay, you got it about a Executive assistant and they went but but or chapter by chapter each week and it was really foundational but I so we have a book club to Look in slack, you know, and it's like the the team is reading all kinds of stuff all the time and some of it is out of my Read strategically category. I say every once every three years. I read fiction And my wife we went on vacation a couple weeks ago and she was like, did you buy a fiction book in print? I'm like, no And I know why she's saying that she says because I'll get hooked and obsessed on the fiction book And if I do it on print, I don't have the kind of where I can switch back and forth and go this Uh, I want to get something else. So every three years like I'll dive through Harry Potter Pretty books not necessarily work related that like one thread cover to cover and you tell everyone like oh my goodness You have to read this book Well, it doesn't have to be But just like a book that you feel has really changed your life non business related The power of me I put up there Um, was really The the list I have to talk about on my my personal site. Those are the ones I go. This is the book you read These are the sets of books. I would probably read every year. I don't necessarily but I'm saying that I would go back to refer to like I'm writing well Like that, um, I don't know. Am I answering your question right? Maybe I really love the Harry Potter series I didn't know before five, but the first three a place through And I want to get a Harry Potter world so Better yep, thanks


Hello, welcome to the video session on AM receivers, myself SN Chamath Gauder working as assistant professor in electronics and communication engineering, Walsh and the Institute of Technology, so on. In this video session we are going to study about the envelope detector and TRF receivers. This is the learning outcome at the end of this session students will be able to describe the envelope detector and TRF receiver. Pause the video for some time and recall which are the types of AM generation techniques. I hope you have recalled the types of AM generation techniques here. Now, let us proceed with the video session, this circuit is an diode detector, it is also called as envelope detector, it is also called as AM dot demodulator. This circuit consists of an input transformer, diode and RC filter circuit here, as you can see in the diagram. Now to understand the working principle of this circuit, let us divide this into two parts. So, first part consisting of a input AM signal, input transformer and a diode, in the second part let us consider this RC filter circuit here ok. So, AM signal is given to the primary winding of the input transformer and due to the variation in the current, a voltage is been generated in the secondary transformer, secondary winding of the input transformer and this voltage is given to the diode here ok. So, as we have studied the half wave rectifier circuit, in the half wave rectifier circuit, the same circuit is used for the half wave rectifier circuit. Here the diode is connected in such a way that the diode conducts current during the positive half cycle and do not conduct current in the reverse bias condition ok. So, in this circuit also the diode conducts during the forward bias and do not conduct during the reverse bias ok. So, here as I said we will divide the circuit into two parts ok. First part is a rectifier part and second part is the envelope detector part ok. Envelope detector in the sense it is a RC filter circuit ok. So, AM wave is given as an input to the rectifier circuit and half cycle we will get at the output end and this signal is given as an input to the envelope detector and we will get the envelope of the input signal here ok. So, in the signal we can see that there are two envelopes, one is the upper and second one is the lower ok. Here it consisting of a high frequency carrier signal here ok. Now, as I said as I said in the in this circuit the diode conducts during the forward bias that is during positive half cycle of the AM signal and diode is reverse bias during the negative half cycle during which the diode will not conduct ok. So, here in this diagram we can see the carrier signal which is having both positive cycle as well as the negative cycle ok. So, when the carrier signal is positive going during that time diode conducts and it is passed through the diode and this waveform comes at the output terminal of the rectifier circuit ok. So, during the negative half cycle the diode is reverse biased hence that negative cycle does not appear on the waveform at the output terminal of the rectifier circuit here. So, here only positive cycles are passed through the rectifier circuit and it appears across the output terminal ok. Once we get the half waveform at the output terminal of the rectifier circuit this signal is given to as a input to the envelope detector. Envelope detector detects the envelope present on the high frequency signal we will see in detail in the next slide. Here you can see there are current pulses which are only positive cycle here negative cycle is not present in this waveform ok. So, now in this circuit as I said the envelope detector consists of a capacitor and a resistor ok. So, here when the positive cycle is applied across the diode conducts and that current appears across this capacitor and resistor ok. Now when the voltage appears across the capacitor the capacitor gets charged to the peak value of that current pulse ok as well as that voltage also appears across the resistor here ok. As I said in the reverse bias diode do not conduct ok. Now when the level input level of the signal goes below the capacitor level the diode is reverse bias we will see that in this waveform here ok. In the first current pulse you can see when the current pulse is positive diode conducts and the capacitor starts charging here up to the peak value. Once the input signal decreases below the level of capacitor the capacitor starts discharging through the load resistance ok. This process continues till the next positive cycle. Again when the input signal increases the more than the capacitor level again capacitor starts charging up to the peak value. When the inputs level decreases below the capacitor value it starts discharging here. In this way this process continues till the input signal is present and the RC filter circuit goes on detecting the envelope of the AM wave here ok. This is the entire waveforms here as you say as you can see the first waveform is the AM output AM input waveform and second one is the output of the diode circuit and this one is the output of the RC filter circuit. Second receiver is the TRF receiver this is the block diagram of the tuned radio frequency receiver. Here you can see there are multiple stages first this is the antenna, first stage RF amplifier, second stage RF amplifier, detector, audio amplifier, power amplifier and this is the loudspeaker. Now as we can see between the antenna and the detector there are n number of RF amplifiers. For our convenience we have used only two stage RF amplifiers here. Now here below that you can see there are dashed lines which are connected first RF amplifier, second RF amplifier and detector circuit to this ganged tuning knob ok. Now these three blocks are connected mechanically to a ganged knob here which is used to tune these blocks to a particular or selected frequency ok. Once antenna receives the electromagnetic signals which are present in the atmosphere and then gives those signals to the first stage RF amplifier. The ganged we use this ganged tune to select a desired frequency and this RF amplifier amplifies that desired frequency and rejects all the remaining signals here. Once it is amplified then it will be fed to the second stage amplifier. Second stage amplifier again it is used to amplify the desired signal and reject the remaining signals. Once the desired signal is amplified to a desired level then it will be fed to the detector. As we have seen in the earlier in this video session regarding the detector detector detects the envelope present on the AM wave. So this block or this stage detects the envelope present in the AM wave and the it recovers the original signal which is present in the AM wave and it will be fed to the audio amplifier. Audio amplifier increases the power level of the signal again it will be fed to the power amplifier. This power amplifier also increases the power level of the recovered signal and then it will be fed to the loudspeaker.  What is this tracking of tune circuit? As I said ganged tuning knob is used to vary the frequency connected to the variable capacitor. It is expected that all the capacitor value used in the first stage RF amplifier, second stage RF amplifier and detector are equal but practically it is not the case that is why this problem occurs tracking of the tune circuit. Second thing is the instability instability in the sense it is the case of selectivity and sensitivity. Selectivity in the sense it is the capability of the signal to select the desired signal and sensitivity in the sense to capture the weakest signal present in the atmosphere. Now third one is the variable bandwidth. Variable bandwidth increases the bandwidth of this TRF receiver increases has the frequency increases. So these are the three basic problems which are present in the receivers. So to overcome these three problems we will study the super heterodyne receiver in the next video session and this is the reference thank you.


My name is Beatrice, I'm the service manager for the Child and Adolescent Bereadment Service, which is an NHS service based at North Hampton General Hospital and we outreach into primary and secondary schools offering pre-bereadment support and bereadment support. My name is Helen, and I'm one of Beatrice's Councillors. So I get asked a lot about how can we support children who, you know, who suffer a close family bereadment. It's basically creating a safe space where a child can tell their story and having acknowledged by an adult i gael i'r anodol tidig sydd wedi bod nid iawn o'r chael a chi'n credu'r eistedd cynhyrchu a ddych chi'n gwybod i'r eistedd cynhyrchu'n gwybod i'r rai yn adwedd i'r yw'r gael erud fawr hefyd.  We'll have our own opinions but that child tells the story about how I feel about the death of a parent, my pet or somebody significant and its that safe space for that child to be heard. And the kind of thing that sometimes people say to me is I'm worried that if I get them talking about this they're going to get really sad, really upset, I'm going to make things worse. Actually children look to adults to role model grief behaviour, I'm a great believer that children should have the choice to attend funerals they have the right to say goodbye to somebody they love has died. acします should be how to behave. So I say do get angry, ac sadd, and upset because you're saying that all these feelings are okay. Old enough to ask, old enough to be told, that's my kind of key message. chegar gwrOT o na dim y maireach a'i ddau gyda hyn? I think it's very interesting, the comment you just made about you're not being able to say certain things and very often in the course of my discussions at child we'll say I don't like to say things at home Sesame seeds at that that will upset mum or dad, so they keep all this stuff inside of them. It's lovely at them that as councillers we are able to go into school, have that time with them, have that safe space and create a relationship where they are able to express themselves. It's just really important building a relationship with them and letting them just express themselves. We use the book with all the children we offer journals so very often if they don't gyda'r cynhwys o'r cyflwysig ynghylch a swolegu'r gwneud yn gyfer cael eu dystyn nhw'r byf yn gwneud. Na ydy'r cyflwysig sy'n cyho ymgylch yn gyfer fwy o'n ymgylch ond ein cyflwysig y gallwn y cou i'r argyn已ol. Cyn nhw'n rhoi yma chi dweud bod hyn mae'n cael ei ddweud, mae'r grannwch yn gan unrhyw i gael ei moseifanodd. Rydym ni'n cael ei ystod trwy ei gael ei ddweud? Ynbaid os gallai'n gweld eu rhoi ar gweithreit? Maen nhw'n gwneud am hynny'n mynd? Nawr, y mynd yn ychwanegineb, a ond nesaf a gydagwyd. Yn rhan fyddion wedi cael ei zoo? Rhyw gynnwys wedi cael ei gweithi, os rydyn ni'n wrthos oes gwrs daethau a gair o hyn ynny. Mae'n gwybod iawn, wedi cynnig o hyn, mae'n gwybod iawn. Ond efoedd hyn gyhoedd, wedi bod gwybod iawn. Efallai efallai eich gyrfa gwyb yn hyn ymgyrch, a'r bwysig a phoedd eich ddych chi. Rydyn ni'n dweud yn wneud, os ti'n gofgoniarnodd, fydd y期ffer iawn i ddweud i gael yllil yn hyd agnod yn ffii hyn fyd. Mae'r rhai yn ei ysgol iawn i gyda mewn llawer yn gy问. Rydyn ni'n siarad yn ystod bod ni'n fynd i gael y sgol rhai, dyfawr o'r ffiaeth yn ei ddweud. Rydyn ni'n maes i gael penderfyn iawn, mae yna gweithiau ei nhw. Mae'r rhai yn mynd i'r gael ar gyfer amser i gael a fyddwn ni, oherwydd byddwn ni'n maes i gael ysgol. gadget. It's such a massive thing for a teenager or a young person who's going around their day-to-day business and they're grieving, they're carrying this massive weight that there's an awareness, that teachers are aware that they are not excusing bad behaviour but just, there is an openness within the school and that they are able to talk and express themselves there. they are able to talk and express themselves there. For primary aged children, we use a variety of resources, we've got workbooks, these are produced by a charity called Winston's Wish, so these are art and craft workbooks, but they're slightly older child. We have the same sort of thing, but it talks more about feelings and these are a very familiar thing that we can teach school staff to use. We've got a lot of books about, this is a very old one, books about animals that have died off from a really useful tool basketwg, er mwyn amser o開ioedd y pwysigredig o fe ddّador iawn o windowa pwysig, ac mae gennym du eu lle. Dyma ni'n cwrs iawn i wneud, mi wnaeth gan roedden yn meddwl, a ddaredd, ddaredd... Ddareddau. Mae ddartoddiad yn ei ffordd, wedi gŵr? Yna llawer o ddod o ddardgwaf, rwy'n cefnod. Mae'n ddartoddiad o fe ddardgwaf, rwy'n cefnod, ac mae'n ddardgwaf yn ei ffordd ffordd o ..y'r cyflwyll y ddefnyddio cymunedol yn ysgrifennu.


Let me fill up a few gaps in the last lecture. So, for example, this was, I had discussed this card game, bridge game. There was an example, number 2.7, which was talking about game of bridge, in which 26 cards have been dealt to people, to the players A and C. So, remember there were 4 players A, B, C, D. So, 26 cards have been dealt to the players A and C with 7 clubs. So, we wanted to compute the probability that player B gets 4 clubs. Now, I was trying to say that this can be, I was trying to show this as an example of computing a conditional probability, that is, already 7 clubs have been dealt to players A and C. So, what is the probability of getting, B getting 4 clubs. But now, I wanted to then show you that, of course, we solved out the problem. I told you that this is the probability, but then it was not possible to explain this through the conditional probability argument. So, therefore, I just want to tell you that there are other ways of computing this probability and that is by reducing the sample space. So, now, instead of taking the distribution of 52 cards to the 4 players, I am just reducing the sample space, because 26 cards are now left out of which 6 are clubs, because 7 have already been distributed to players A and C. So, then this is now your multinomial distribution. So, what you are saying is that out of 6 clubs, B should get 4 and then from the remaining 20 cards, he should get the other 9 cards. So, that way he gets 13 cards. So, this is the number of ways in which he can get 4 clubs out of 6. And 9 cards out of the remaining other 20 cards. So, this is the number of ways in which he can, this can happen and the total number of ways in which he can get 13 cards out of 26 is 26 choose 13. So, this is the actual probability and this we can get by reducing the sample space. So, this is another technique which is very helpful at times. You can very easily compute the required probability by doing this. So, you do not have to always go through the formula, at the actual formula. You can always play around with alternative ideas also. Now, remember I asked you to construct examples when we were talking of independence of 3 sets. And in that case, I showed you that there are 4 conditions which have to be satisfied before you can say that the 3 sets are independent and then I asked you to construct a counter example to show that suppose the first 3 are satisfied, the last 3 are satisfied. That means, pair wise if you choose any 2 sets from here, they are independent. They satisfy the condition of independence. That means, your probability of E intersection f is p e into p f, probability of E intersection g is p probability of E into probability of g. And similarly, probability of f intersection g is a product of the probabilities p f into p g. So, you can construct situations where let us say last 3 conditions are satisfied, but the first one is not satisfied. And so I have been able to lay my hands on this example here. Suppose, your sample space consists of these 4 numbers. So, when each number is equally likely, that means, the probability of any number coming up as a result of the experiment has probability 1 by 4 because they are equally likely and there are 4 elements in omega, your sample space. Now, let us choose E to be as consisting of the numbers 1 4, f to be consisting of the numbers 2 comma 4 and g 3 comma 4. In that case, you see if you see the probability of p e, p f and p g is 1 by 2 because they are 2 numbers totally 4. So, 2 by 4, again we are using the same concept because outcomes are all equally likely. Therefore, I am using the m by n version of the probability and so this is half for each of the sets. Then, probability E intersection f, now E and f have only 4 in common. So, that is one singleton and that probability is 1 by 4 which is the product of p e into p f. So, similarly you see that the pair wise independence has been, you can easily verify that the 3 sets are pair wise independent. But, when you write E intersection f into intersection g, that again results in single number 4 and so this probability is 1 by 4, but this is not equal to p e into p f into p j which is 1 by 8. Therefore, now you get an idea and you should try to construct one example of your own to show that a pair wise independence of 3 sets is not enough to say that the 3 sets are independent or 3 events, I mean the 3 events are independent, you should be able to construct. And then I said that you know extending this becomes little more cumbersome and so you will leave it here only. Now, exercise 2 of course, I have given you the corrected version. So, this is there and question 10, in exercise 2 I want to revisit because when I was reading it last time I said that this needs a little thought and so let us revisit the problem. So, actually you were given the data that a battery as a lifetime. So, there is a probability that the battery will last for more than or equal to 10,000 kilometers that probability is given to be 0.8 and the probability that it will last or equal to 20,000 kilometers the probability was given as 0.4 and then that it will last more than or equal to 20,000 kilometers also a probability is associated with it. And you were asked to find that if you have bought a battery which is already run for 10,000 kilometers, what is the probability that will be running for more than 20,000 kilometers. That means, its lifetime will be more than 20,000 kilometers if it has already run 10,000 kilometers. So, this is a simple case of conditional probability computing the probability that the lifetime. So, if I let L denote the lifetime of the battery, we are wanting to compute the probability conditional probability of the event that the lifetime is more than 20,000 kilometers given that it is already 10,000 that is it is already 10,000 kilometers old the battery it has run that much. And so by a formula now when you take the intersection of these two. So, obviously this is a subset of this and therefore, the intersection simply becomes L that means you are wanting the lifetime to be greater than or equal to 20,000 kilometer when it is already run for more than 10,000 kilometers. So, the intersection of these two would be this because you want the battery to run 10,000 kilometers and you want the battery to run 20,000 kilometers. The intersection would mean that you want the battery to run for more than 20,000 kilometers. And so this is divided by the probability of this event which is L greater than or equal to 10,000 and therefore, this is equal to 0.4 by 0.8 which is half. So, this is the so I just thought that if you have thought about the problem maybe you some of you have already done it, but then this is the right answer. We have talked of conditional probability, but I just thought that should formalize this some more in the sense that you see we are defining now given an event A then we are computing the conditional probability of events conditioned on F. So, to show that this is the function that you have defined here the conditional probability function satisfies the three axioms of probability and not too difficult to compute to show because first axiom requires that this for any event E the conditional probability with respect to F must be within 0 and 1 that is the first axiom. So, here if you take probability E condition on F then by definition this is this. Now, you see that E intersection F is a subset of F. This is a subset of F and therefore, we have already shown remember after giving the axioms we proved some propositions and there I showed that if a subset is a subset of another subset then the probability would be. So, that means, here probability E intersection F will be less than or equal to probability F because this is a smaller event in the sense that this is a subset of this therefore, probability of this is less than or equal to this as we could easily show. Then and by definition of course, probability E condition F is non negative this is non negative this is non negative. So, this is non negative. So, therefore, the first axiom is satisfied because the P intersection F is less than P F. So, I divide by this this is less than 1 and this is non negative. So, first axiom is satisfied. Now, second axiom said that your probability omega should be 1. So, here for us because we are conditioning on F. So, the corresponding axiom would be that probability I should have write sorry sorry this should be again same thing I have to say that omega condition on F. So, what will this be this and therefore, now when you take omega intersection F this will be probability F this is equal to 1. So, therefore, probability F divided by probability F is 1. So, probability of omega condition on F is 1. So, the second axiom is satisfied and the third one requires an E I intersection F divided by P F. Now, this I can write as see here this is this then because distributive law holds this will go as this can be written as union E I intersection F I belonging to I this thing. Now, because E I intersection F are disjoint since E I's are disjoint I have taken a sequence of disjoint events E I's here. So, E I intersection F are disjoint and so by and probability P the probability function the original probability function satisfies axiom 3 and therefore, this can be written as summation of probabilities E I intersection F divided by P F right which is equal to. So, this can be written as summation probability E I condition F I belonging to I. So, the third axiom is also satisfied therefore, the conditional probability function is also a probability function that is it satisfies the 3 axioms. Now, again I just want to continue working because conditional probability function is a important concept. So, again a little elaborated example that I would be 2 gamblers. So, this problem would be coming after I define for you the conditional probability. Now, I want to discuss the gamblers rho n problem which is the interesting example of conditional probability use of conditional probability. So, let us see the 2 gamblers A and B and they bet on the outcome of the toss of a coin right. Now, if on each toys if on each toss if h occurs that means, if the head shows then A collects 1 unit from B and if tail occurs that means, if T occurs then B collects 1 unit from A. So, this is all a simple game you toss a coin and then if the head shows A gets the money and if tail shows B gets the money from A. Now, tossing of the coin continues till one of them runs out of money. So, that is the gamblers rho n right. So, one of them will end up with all the money and the other one will have no money left. So, suppose total money is 15 units I am just taking a number 15 you will see that through the solution it does not matter whatever the amount of money that they start with and A has I units. So, that means, B will have 15 minus I units within. Now, tossing of the coin are independent events and we are assuming that the coin is biased. So, if a probability h is P and probability is 1 minus P we will also consider the case when P is half. Now, we want to find the probability that A ends up with all the money and we have assumed that starting at the starting point A had I units of money within. So, let E be the event that A ends up with all the money and let P I denote the probability because we are starting the game when A had I units. So, I am just denoting it by P I which is the probability of E ending up with all the money and A had I units to start off. Now, we have been using this technique very often because you are when you are tossing a coin your sample space is consisting of just h comma t two points in the sample space. So, you can write P E in terms of conditional probability P given h and that means now this we are saying that we are starting the game. So, the first toss of the coin either results in h or in t. So, this is conditional of E that means this is the probability of E this is the event that A ends up with all the money starting with I units when the first toss results in head. So, this is that event right. So, that into P H plus this is again the similar interpretation that A ends up with all the money when the first toss of the coin shows a tail. So, this is this into P T. Now, when the first toss of the coin gives you head then A collects one unit from B. So, therefore, the money at the end of this after the first toss A ends up with money I plus 1 and if the first toss shows a tail then A will have to give one unit of money to B and therefore, he will have I minus 1. So, therefore, if I as I said in the beginning I am denoting this by P I because A had I units of money when the game started. So, therefore, this equation can be rewritten as P I is equal to P I plus 1 because this will be then the probability that now A has I plus 1 units and you want to compute the probability that A ends up with all the money right. And then this into P probability of getting a head then here A will lose one unit of money to B. So, it will be P I minus 1 into 1 minus P. So, 1 minus P we can also write as Q now I can since P plus Q is 1 I can multiply this by P plus Q and write this equation in this way right and then rearranging the terms that means, see P I plus 1 minus P P I I bring here and P I minus Q I take to this side. So, I get this equation right and that gives me that P I plus 1 minus P I is equal to Q by P into P I minus P I minus 1. So, I get a recursive relationship between these P I's and boundary conditions are that if P had no money to obviously, the probability of his ending up with any money is 0 because he will not be able to play the game right. So, P 0 is 0 and P 15 because the moment he has 15 he has won the game and so the probability is 1. So, P 15 is 1 and P 0 is 0 right. So, therefore, now you we use this recursion and we start with I equal to 1.  So, P 0 is 0 and therefore, I get this equation then when I put I equal to 2 in this recursion I will get P 3 minus P 2 equal to Q by P P 2 minus P 1, but P 2 minus P 1 from here is Q by P P 1. So, it will be Q by P whole square P 1 and so this way you can go on writing the differences. So, P 15 minus P 14 will therefore, become Q upon P raise to 14 because whatever the number here that is 1 less than this. So, the power of Q by P is 14 into P 1 right. Adding up P obtained. So, now I add up all these equations then you see these things will cancel out in pairs and you will be left with P 15 minus P 1, but P 15 is 1. So, this is 1 minus P 1 is equal to and on this side Q by P you can take outside. So, it will be 1 plus Q by P plus Q by P whole square and so on up to Q by P raise to 13 into P 1 right. And now this is a geometric series I can write down the sum. So, this will be 1 minus Q by P raise to 14 in upon 1 minus Q by P. Now, this is a finite geometric progression. So, therefore, it does not matter the only thing I need is that I can do this if Q by P is not equal to 1 right because otherwise I will be dividing by 0.  So, we consider the case when Q by P is not 1 in that case what we got from the last slide is 1 minus P 1 is Q by P 1 minus Q by P raise to 14 upon 1 minus Q by P using the geometric progression series sum.   And so the required probability again from your recursion equations you will immediately get that required probability P i that means when A started with i units of money would be 1 minus Q by P raise to i upon this because that sum will be up to Q by P raise to i minus 1 and so you will get this.  So, now if you want to find the probability that B ends up with all the money replace P by Q and i by that means right because now for B the P is Q and the money that B starts with this 15 minus i. So, when you make these two replacements you will again get the formula for computing the probability that B ends up with all the money right. Now, again continuing with some more results on conditional probability. So, this is proposition 2.5 what we are saying is that suppose you are given that conditional probability of A given B is 1 then you can show that conditional probability of B complement given A complement is 1. So, here I could have also given this as an exercise, but I just thought I will show you some more ways of doing it and then you can apply it to for example, I think you can show that conditional probability of A complement given B will also be you can compute or that will be independence fine right. So, right now just look at the definition. So, the conditional probability of A given B is given by this. Now, since this is equal to 1 it follows that probability A intersection B is P B. So, the moment you get this result you can see that a probability A union B which is written as P A plus P B minus P A intersection B this will because this thing is 0 P A intersection B minus P B. So, it reduces to P A. So, therefore, your probability A union B reduces to P A right and therefore, when you take the complement of A union B. So, probability of A union B complement will be 1 minus P A which is nothing but P probability of A complement and so and then again by your D Morgan's law we had seen that A union B component will be A complement I mean complement is A complement intersection B complement. So, this probability is therefore, probability of A complement right and hence your probability of B complement conditioned on A complement is this. Now, since these two things are the same therefore, this reduces to 1. So, one can go on and therefore, now the idea would be that you should get interested enough to try out many more results related to conditional probability solve more examples. Now, final result on conditional probabilities now this is conditional independence remember we defined independence of two events if the probability of the intersection of the two events is equal to the probability of the product of the individual probabilities. Now, is same thing gets extended. So, we say that E 1 and E 2 are said to be conditionally independent given that event f has occurred. So, if probability E 1 conditioned on E 2 intersection f is probability E 1 conditioned on f. That means, the occurrence of E 2 the same definition that we gave for independence of two events occurrence of E 2 has no bearing on this probability. So, that means, you when you condition it on E 2 intersection f it is the same as conditioning on f and E 2 has no role to play right. Now, in fact so we will just write it out in a. So, this is one definition, but you can come to a better result and this is we say that E 1. So, therefore, by definition E 1 condition E 2 intersection f this probability can be written in this way right. And this is given to be by the definition of E 1 E 2 being conditional independent conditional independent. This is probability E 1 conditioned on f right. So, therefore, from these two you get that this probability is equal to E 1 f and this probability of E 2 intersection f I can write as E 2 conditioned on f into P f right. So, this is the result and this one also again now I can condition on f. So, this will be probability E 1 intersection E 2 conditioned on f into P f and this. So, P f P f cancels out because remember whenever you talk of conditional probability with respect to an event then that probability has to be positive otherwise you cannot define it. So, of course, it is understood that P f is greater than 0. So, therefore, I can cancel out P f here and I will be left with probability of E 1 intersection E 2 conditioned on f is the product of the individual conditional probabilities that is probability E 1 conditioned on f into probability E 2 conditioned on f. So, this is you just extend the original definition of independence of two events to in the same way and. So, I will take up now an example a little elaborate example to show you the use of conditional independence. After defining conditional independence of two events with respect to the occurrence of another event I will now take up this example it may look a little complicated, but it shows good use of conditional concept of conditional independence. So, here again this example I have taken from Sheldon Ross. Surprisingly, this book this I will give you the reference later on has lot of new and innovative examples and therefore, I am using quite a few of them here in this course. So, now consider the situation when there are k plus 1 coins in a box right and you the probability of choosing the i th coin shows they are k plus 1 coins in the box and if I pick up the i th coin and toss it then the probability of it is showing a head i th coin shows a head is i by k and i varies from 0 1 to k. So, that means you can see that even i is 0 that means if you pick up the 0 th coin then the probability of it is showing a head is 0 which means both sides must be tails. Then if you choose the if you happen to choose the second coin the probability of it is showing a head would be 2 by k and similarly, the if you choose the k th coin if you choose k plus 1 th coin which has the number k then the probability of it is showing a head would be k by k which is 1. So, probably this particular coin the k plus 1 th coin is having head on both sides. So, whatever it is the situation is this now a coin is randomly selected from the box and is repeatedly tossed this should be repeatedly l y if the first. So, let me just make the correction here. So, it is repeatedly tossed if the first n tosses all result in heads what is the conditional probability that the n plus first toss will also result in a head. So, that means I pick up the coin at random from the coins which are there in the box then I repeatedly toss it and if the first n tosses have shown heads then I want to compute the probability that the n plus first toss will also result in a head. So, let us see we start computes finding out how to compute this probability. So, suppose C i is the event that the i th coin is initially selected and this could be any of the 0 1 2 k numbered coin. Then f n is the event that the first n tosses resulted in heads this is the and then h is the event that we want. So, n plus first toss results in head. So, I want to compute the conditional probability of h given f n given that f n has occurred. So, we have had n tosses and now I want to compute the probability that the n plus first toss will also be a head will show a head and this is the expression. So, I am going to derive it for you since 1 of the k plus 1 th coin will be selected. So, then f n can be written as f n union C i because at least one of the coins. So, this probability of C i union C i varying from the root k will be 1. So, f n can be written as f n union i varying from 0 to k C i and therefore, probability h conditional f n which is can be written as this. Then from f n I can write this expression union f n intersection C i and again by the distributive property of intersection and union I get that this can be written as probability of union i from 0 to k h intersection f n intersection C i. Because this is this is this and then this because you see all the C i's are mutually exclusive because one of the coins will get selected. So, therefore, these events become mutually exclusive and so the probability of the union can be written as some of the probabilities i varying from 0 to k h intersection f n intersection C i divided by p f n. Now, this one I can write in terms of conditional probability as h condition f n intersection C i into probability f n intersection C i divided by p f n. Then this remains this again I can write in terms of conditional probability C i condition f n into p f n.  So, therefore, probability f n cannot be 0 and so I get this expression which is written here. Now, it is reasonable to assume that repeated tosses of the ith coin are conditionally independent. This is where I am using the concept that means repeated to assume that the repeated tosses of the ith coin are conditionally independent respect to f n. That means, see I am considering the case when a coin was picked up randomly then it resulted in n tosses showing heads and now when I toss further. So, then they will be independent of conditionally independent of f n which means that probability h condition f n intersection C i is actually probability h condition C i only. So, f n has no real role to play here. This is what our definition of remember we said that e 1 given e 2 intersection f if I wanted to say that e 1 and e 2 are conditionally independent respect to f given that f has occurred. Then this is probability e 1 sorry f that means e 1 and e 2 are conditionally independent when f has occurred. So, then e 2 has no role to play on the occurrence of conditional happening of e 1 given f on the. So, the probability would be independent of the event e 2. So, the same thing here we are saying that here f n because it is conditional on f n. So, this probability is the f n has no role to play here and so probability h given C i. So, this is what we are assuming here and therefore, each of this probability is i by k. So, now that means I can now apply this in the formula here and this is i by k. So, that means you are getting because you have got n heads have shown up and probability of each head is i by k and I am assuming that the tosses are conditionally independent. So, therefore, this is i by k raise to n and the n plus first toss gives you a head will be 1 upon k plus 1 because there are k plus 1 points there and so sorry. So, this probability is what am I writing here yeah C i f n. So, h given f n. So, let me just check out here this is C i f n right. So, a probability of picking up the ith coin. So, again if you just pick up the ith coin that probability should be 1 upon k plus 1 because any of these coins are equally independent a coin is randomly selected. So, that means any of the coins is equally likely when you pick up from the box. So, therefore, the probability of picking up a coin is i by k plus 1. So, therefore, this becomes this and similarly here yeah. So, actually what is happening is that C i f n yes I missed out on this part. So, probability C i given f n I have rewritten as this. So, this is probability f n condition C i into P C i and then this is sigma j varying from 0 to k f n. So, the probability f n I am writing in this way f n condition C j into P C j. So, this is where. So, now probability f n given C i as since the things are conditionally independent the probability of picking up a head remains the same. So, when you want to pick up n heads this will be i by k raise to n and probability C i will be 1 upon k plus 1 and then here similarly this is summation. So, j varying from 0 to k j by k raise to n and 1 upon k plus 1 because now here your j is varying this corresponded to the ith coin that you have chosen. So, this is the thing and. So, it is just a computation I wanted to show illustrate maybe you can say that it is a engineered problem or whatever it is, but somehow you could use make use of the concept of conditional independence and arrive at this result and again through methods of calculus you can actually show that if k is large then this probability is approximately equal to n plus 1 upon n plus 2. So, therefore get simplified when you have a large number of points in the box, but otherwise yeah. So, this were continuously you broke up the. So, here in this expression yes C i's conditional f n this also I had to rewrite in this decomposed form and then apply the probabilities to get this expression. So, that was missing here yeah fine. So, this is an example to and often there will be situations when you would coming across the concept of conditional independence. Let me discuss exercise 2 with you again I will just try to give you brief hints. So, anyway probability the question 1 says that you have to compute the probability that only exactly 1 of the events e and f occurs and that is equal to probability e plus probability f minus 2 and of course, when we say minus 2 probability e f that means e intersection f. So, that notation is also acceptable you do not write the sign you know the intersection sign you simply say e f. So, that is what it means right. Now, if e f and g are 3 events then you have to find expression. So, again I am just wanting you to be familiar with the how you write express events in terms of your complements union and intersection. So, here I want you to write find expressions for the events. So, that of the 3 events e f and g only e occurs. So, if you want to write this then in 2 you have to write exactly 2 of them occur right exactly 2 of them occur. So, the third one should not occur. So, you can imagine that you will have to use unions and complements right. Now, in question 3 this is actually very simple the slash sign the condition sign is sort of dim, but anyway. So, this says that if probability a is greater than 0 then show that probability of a intersection b condition on a is greater than or equal to probability a intersection b condition on a union b. So, that is very straight forward actually and now you have to show that p of a intersection the conditional probability of a intersection b given a is greater than or equal to probability of a intersection conditional probability of a intersection b given that a union b has occurred. So, it is very simple because you see a is a subset of a union b and as we have already discussed that probability of a union b will be greater than or equal to probability of a right. And in the left hand side when you compute the conditional probability you will have a in the denominator in the denominator the numerator is probability a intersection b because a intersection b intersection a is again a intersection b. So, this is what actually you have to figure out and similarly on the right hand side the numerator is the same, but denominator would be probability of a union b and since probability a union b is bigger or equal to probability a you have the required inequality. So, I just gave it to you to be able to just you know figure out these things and therefore, then you can answer the question. So, if you write out the expressions you can immediately give the answer to this question. Now, problem 4 is from Sheldon Ross actually it should say Sheldon Ross or Ross Sheldon. In answering a question on a multiple choice test you know where you have more than one choice and you have to take the right one a student either knows the answer or she guesses. Let P be the probability that she guesses assume that a student who guesses at the answer will be correct with probability 1 by m where m is the number of multiple choices right because if she is guessing she does not know. So, each any answer out of the m choices any one of them is equally likely. So, the probability is 1 by m what is the conditional probability that a student knew the answer to a question given that she answered it correctly and I have given the answer here. So, know what are we saying what is the conditional. So, please enter probability what is the conditional probability that a student knew the answer to a question given that she answered it correctly. So, use the concept of conditional probability and then you should be able to do it right and now again this problem is from Sheldon Ross. At a certain stage of a criminal investigation the inspector in charge is 60 percent convinced of the guilt of a certain suspect. So, his conviction is that the 60 percent that means 0.6 is the probability of the person being guilty. Now, suppose that a new piece of evidence shows that the criminal has a certain characteristic such as left handedness, boldness, brown hair etcetera. So, it turns out that through some eye witness who may have seen the criminal some doing the act. The eye witness can only say that the person was either left handed one of the conditions characteristics is owned by the criminal. So, is uncovered. So, through some facts it is found out that whoever committed the crime has one of the characteristics right. If 20 percent of the population possesses this characteristic that means whoever in a town crime has taken place and so what they are saying is that 20 percent of the population possesses this characteristic. How certain of the guilt of the suspect should the inspector now be should again instead of how it should be now be if it turns out again S if it turns out that the suspect is among this group. So, now this is the situation for computing the base probability because you see the first the initially the inspector is 60 percent convinced of the guilt of a certain person. Now, it has been known that the criminal possessed some characteristic which it turns out that this suspect has that characteristic. So, therefore the probability of the suspect being a criminal would go up and so the posterior probability after knowing that the criminal possesses the characteristic will go up. So, therefore you want to I want you to compute the posterior probability here. Problem 6 says a parallel system functions whenever at least one of the components work. Consider a parallel system of n components and suppose that each component independently works with population 1 by 2. Then the conditional probability that component work 1 works given that the system is functioning. So, here you have to use concept of independence and conditional probability. So, problem 7 says that you have to either prove or give counter examples to the following statements which are self explanatory you should be able to either show that the statement is valid otherwise you construct examples to show that it is not. Now, problem 8 we I am asking you to show that if e f and g are independent then you have to show that e is independent of f union g. See remember now here I am using the definition of 3 events being independent. So, you have these 4 conditions that will be satisfied and then you can easily show that e is independent of f union g. In fact, you can whatever subsets you find by operation of you know taking intersection union or complement and then taking operations on those you can show that e will be independent of any of that any of such event which is founded by which is obtained by doing the operations of intersection complement and so on from f and g. So, this is what we are saying here. Now, store a, b and c have 50, 75 and 100 employees and respectively 50, 60 and 70 percent of these are women. So, that means store a has 50 employees and of which 50 percent are women. So, you can immediately say that 25 are women similarly 75. So, 60 percent of the employees in store b are women and then 70 percent of the employees in store c are women. Resignations are equally likely among all employees regardless of sex. One employee resigns and this is a woman what is the probability that she works in store c. So, now here again I am asking you to use base formula to compute the probability. So, one employee resigns that is given and this is a woman. So, this is also given that means a woman employee resigns you have to find the probability that she works in store c. 10, the probability that a new car battery functions for over 10,000 kilometers is 0.8. The probability that it functions for over 20,000 kilometers is 0.4 and the probability that it functions over 30,000 kilometers is 0.1. So, these are all conditional probabilities. If a new car battery is still working after 10,000 kilometers what is the probability that it is total life will exceed 20,000 kilometers and then it is additional life will exceed 20,000 kilometers. So, problem 10 we will have to answer may be we will leave out problem 10 from here and we will revisit it later on, but problem 11 you can answer easily. Suppose that a person chooses a letter at random from reserve. So, instead of chosen it will suppose that a person chooses a letter at random from reserve that means it can be any of the letters R, E, S, V and then chooses one at random from vertical. What is the probability that the same letter is chosen? So, this of course is your earlier from counting the probability in the number of combinations that are favorable to this thing that means see the two letters that are common between these two words are R and E that is it. So, you have to now find out the number of ways in which R will get selected from both both or E will get selected. And you can see that for example in the first word reserve R appears twice out of you know R E S E R V E and R in vertical appears only once. So, you can accordingly find out the probabilities and then find out that and since the operation of choosing a letter from reserve and from vertical R independent events the required probability would be the product of these two.


Greetings to the business community and my fellow St. Lucia. As Minister for Commerce, I'm elated to launch Business Month 2021 under the theme propelling business development through technology. COVID-19 has had a significant impact on businesses worldwide including St. Lucia and has caused unprecedented challenges to the supply chain. Nothing in our recent past can compare to the disruptions caused by COVID-19, not even interruptions due to natural disasters. However, one can safely say that a business mentality has emerged from this pandemic over the past year. Greater focus on capacity building, the need to formalize business ventures and appreciation of modern technology to conduct business activities. In-person contact has been limited, especially in activities such as purchasing, working and socializing. Enterprises have been forced to conduct businesses via the Internet. Certainly, COVID-19 has fostered the atmosphere for more e-commerce and remote working. As a result of COVID-19, digital engagement levels have increased exponentially to a point where information and communication technology can no longer be characterized as they may support service. But it is now the principal driver in the business ecosystem. Technology is evolving at a pace where one can truly be left behind. It is therefore imperative that our nation, especially our business community, the micro, small and medium enterprises, remain abreast with the technology at our disposal as well as find ways to take full advantage of these opportunities. E-commerce is an important tool for innovation, competitiveness, job creation and growth. It offers use potential for traders, MSMEs and others to expand their market reach and connect with overseas buyers, suppliers and consumers of goods and services. E-commerce was growing at a very fast rate even before COVID-19. UNTAD asserts that in 2019, about 1.5 billion people shopped online. An increase of 7% from 2018. Also, COVID has further accentuated the shift towards e-commerce as people and businesses have gone online to cope with various lockdown measures and travel restrictions. UNTAD estimates that online shopping as a share of global retail sales surged from 14% in 2019 to 17% in 2020. As it relates to St. Lucia, the St. Lucia Medium-Term Economic Development Plan identifies digital development as a driver of economic growth and competitiveness. While the National Competitiveness Agenda highlights digitization of industries and development of a digitally skilled talent pool as key priorities for improving competitiveness. In response, the Ministry of Commerce, in collaboration with the Development Corporation Fund, the DCF of the Organization of the American States, the OAS signed an agreement to introduce inclusive resilience for an effective recovery with a focus on science and technology for the current cycle 2021 to 2024. St. Lucia's components, retooling micro-small and medium-sized enterprises through innovation and technology, give rise to St. Lucia's Digital Enhancement Program. This program is geared at improving access and dissemination of mechanisms, technology and non-technological tools as well as innovation for MSMEs to support the reactivation of our economy while addressing diverse challenges imposed by COVID-19. With regard to the observance of Business Month 2021, the Ministry of Commerce and the St. Lucia Chamber of Commerce have shared a myriad of activities. One of the Chamber's flagship activities, Global Entrepreneurship Week GEW, will be observed in the week of November 8th to the 14th. The Chamber will soon be sharing its calendar of activities in celebration of the week. However, I want to mention that another activity of the Chamber is a Virtual Business Resource Symposium to be held on November 10th. Further, the Ministry of Commerce through its SBDC will be hosting a few timely activities, including one, a workshop called Lean Converse Business Model, which is a business planning workshop on November 3rd to the 5th. And this consists of three half-day sessions. The Lean Converse is a tool that allows persons to present their business plan in one page. And also use that format for presentation of the plan to the financial institutions and other investors. Trainees would also learn how their decisions affect the profitability of the businesses. The second workshop, Business Startup Essentials, will be held on November 17th. This is a half-day workshop and will introduce newly registered clients and startup enterprises to the basics of business operations in St. Lucia, and also guide them through the administrative and other planning aspects of a new business. The third workshop, Design Thinking to Develop a Business Workshop, will be held over nine mornings from November 18th to the 30th. Design Thinking is a user-centered approach that leads to problem-solving and the development of new ideas. It offers practical and interactive exercises of various methods to systematically realize your dream of owning your business. This is in sync with our government's youth economy focus. All workshops will be conducted virtually and we encourage business owners and prospective business owners, especially our youth, to capitalize on these capacity-building tools. So here again, we can see the significant role that technology plays in the scheme of things. Continuing with the theme, Propelling Business Development Through Technology, the 14th annual St. Lucia-Taiwan Partnership Trade Show will culminate activities for Business Month. This trade show will be held at the Grosselay Human Resource Development Center on November 26th and 27th. The Ministry of Commerce in partnership with the Embassy of the Republic of China-Taiwan will showcase a wide range of goods and services which will allow the business community and the general public to experience the best of St. Lucia and the Republic of China-Taiwan in the ICT business solutions and products. This will give St. Lucia the opportunity to showcase its advancement of business through the use of technology. To complement the ongoing Love St. Lucia campaign, the trade show will also feature the launch of one community, one product. The idea of one community, one product was generated from the one village, one product movement, an initiative of the government of Japan that was adopted by the government of Taiwan. The St. Lucia concept envisions empowering communities through sustainable use of local resources to foster local development and poverty reduction. In closing, we have all experienced the impact of technology, whether it is in our daily lives or in our business transactions. Because of this integration, we need to remain committed to the development of technological avenues which would assist our businesses. At this juncture, allow me to take this opportunity to thank the business support organizations and the ICT-related businesses for their role and commitment in strengthening our MSMEs during this challenging COVID-19 era and beyond. Let us remain focused on improving St. Lucia's technological infrastructure for improved competitiveness and viability. I thank you.


The aroma of chili filled the air at the Sanford Event Center in Bemidji today and it was all for a good cause. For 26 years United Way Chili Cook Off has been a key event for the organization. 24 businesses and organizations got into the spirit of the competition by building sets and wearing costumes while serving up their best chili recipe. The United Way the Chili Cook Off is more than a fundraising event. It's not about the money as much as bringing the community together to watch really what is happening and that's the one thing about United Way that I'll say the generosity and the philanthropy is one thing to giving but it's the involvement of the community. So far the United Way Bemidji has raised over $164,000. Excellent start. If you've enjoyed this segment of Lakeland News please consider making a tax deductible contribution to Lakeland Public Television.