My name is Brittany and welcome back to my YouTube channel. You guys in today's video I am going to be doing an end of the year reflection video of our second year of homeschooling and I have Brielle here with me She's kind of shy right now, but I really wanted to include her in today's video So you guys can really get a full glimpse of all the things she got up to I really feel so bad for my baby girl Because she really has been my full-on guinea pig with her being my first and this is my first time really homeschooling I really had to do a lot of trial and error until I was able to really figure out What Brielle needed from me as a you know homeschooling mom and all the curriculum pieces that she actually did really truly enjoy So you guys we're gonna flip you around and we're gonna show you guys like all the Projects like all the fun things Brielle got up to this homeschooling Okay, you guys Brielle decided she wanted to show you guys her actual flow of the day and what she actually did So we started off our day using math and we chose Saxon math you guys if you are not new here to my channel You already know we have had like a math journey this homeschooling year until I finally figured out what Brielle was looking for in a math curriculum and what was gonna work for her and Saxon math just happens to be the math that worked out for her We utilize Nicole the math lady. So Brielle watches her video lessons in the morning. So she doesn't need me She's able to do this independently The only part she needs me for is this part right here, which is the mental math Good job read that part, which is the mental math and then I check all of her Lesson practice and I check her mixed practice as well when she's pointing to good job So that is pretty much all I do as far as my parent involvement in Saxon other than that She does it on her own. So Bre do you want to show them your math notebooks that you used? So these right here are the math notebooks that she used. She utilized these ones from school Ness, which I absolutely love They have the grit paper in it So she was able to be able to practice being able to copy all of her problems down and be able to solve them So I really love utilizing grit paper for this I mean you don't have to get these bougie school Ness notebooks, but I just love them so much the quality is really really good So we utilize these notebooks for all of her like math work. So in total in Saxon, this was like the most Consistent math curriculum we ever used. So we actually finished off the year doing lesson 64 We completed six investigations and 12 tests. So that is about the halfway point for Saxon I have another video on my channel showing you guys like a full on review of Saxon math and everything like that So, um, right now I'm going to go ahead and let Brielle talk and give you her opinion about Saxon. So Bre what did you think about Saxon? I like Saxon It was better than the other math that we did. It was better than the other math. We did. Okay So what do you think about Nicole the math lady? She's cool and I like how she Explains the video. Okay. You like how she explains the concept. You like how she explains the concept So how does Nicole teach it? She just gets right into it. She gets right into it. Okay. So Brielle likes Nicole the math lady She's at that whiteboard you guys and she just gets right on into the math problems and she's able to do everything So that is Saxon math I'm so happy we found something that Brielle enjoys and as you guys can see Saxon's black and white and straight to the point Okay, you guys the next thing I'm going to show you is all of Brielle's creative writing So Brielle started off her school.  She really enjoyed using this notebook However, after Brielle learned how to type by using typing comm she really stopped using her journal And she started typing up all of her creative writing stories And you guys like I am so proud of this girl of all of like the stories she wrote and she really really Got into writing this school year. So If she didn't have time to do her creative writing right after math She would typically pick up creative writing after in the afternoon So that was just something she did before she had her screen time So these are like all of the creative writing things that she did and I'm so so so proud of her If you guys follow some of my update videos, you would have seen like some of the pieces that Brie Did the months that she did and she worked on them. So Yeah, so Brie, um, how did you enjoy creative writing? Uh, I liked it because I could think of a story and I could write about it You liked it because you can think of story and write about it and I could get inspiration from other stories too Oh, yeah, all the stories you were reading. So yeah, so Brielle really really enjoyed creative writing And this was just a really fun outlet for her to do. Um, this didn't follow any curriculum This was just something Brielle completely did on her own Okay, you guys the first grammar curriculum program that we did was actually fix it grammar and you guys Brielle really really enjoyed fix it grammar fix it grammar is just a really simple grammar program Where she is just going over one sentence a day and she is editing it and she is finding the different parts of speech So uh fix it grammar was kind of like a warm up and also to fix to grammar really came in hand When we finished off our main grammar curriculum a little bit earlier than expected So we pulled out fix it grammar and we really enjoyed doing this And it's just so crazy how they start off in the beginning of fix it grammar Like only being able to identify just the nouns. Yeah Isn't that crazy for when you look at that and then at the end She was being able to identify like the nouns the prepositions the coordinating conjunction She was able just to identify everything and like i'm so so so proud of like all of her hard work And I really enjoyed her using fix it grammar as a good way for her to Really master and hone in on those grammar skills now you guys fix it grammar actually completely revamp their Style of grammar so now each of the days are broken off on each page And the way that they have their new setup is so so so good So we are taking fix it grammar into us on the next year So for fix it grammar, they actually wanted the students to write out their story after they edited In a notebook, but brielle since she got into typing so much She decided she wanted to go ahead and type out the nose tree story. So brie. What did you think about uh fix it grammar? I like fix it grammar and it was like simplifying rotten staff Oh, okay. So it was simplifying rotten staff. So she's kind of already going ahead It was perfect to use at the end of the year because we were starting to get tired Yes, she's right So brielle she pretty much just said that it was perfect using at the end of the year because we were getting kind of tired So this was a great supplement for us to add in now Now fix it grammar to really be honest you guys it can really stand on this own As a full-on grammar curriculum, but as you guys can tell brielle really enjoys writing So I really wanted her to hone in on these grammar skills to really help out with her writing skills Okay, you guys so brielle. She actually utilized rotten staff build an english series as like her main grammar program And we really really enjoyed using this grammar program. It was very thorough It's a mastery based program where each chapter we are going to be going over just one part of speech And I love how it systematically built upon each other Rotten staff really utilizes the diagramming of sentences really heavily Uh, so it's a really completely different opposite approach than fix it grammar However, I love using both of those approaches because at the end of the year After she finished rotten staff and we went back to finish off fix it grammar It was really cool being able to see if she really mastered those skills Or if she was really heavily Reliant on the diagramming to be able to pull out those different parts of speech So as you can tell it's a trim with brielle. She just loves simple basic curriculums Now I will say this uh curriculum is pretty teacher intensive because I do have to go over and read this part with her Um, and then I do the oral drills with her And then she's able to do her written practice and review on her own Most of these lessons we did however do it completely oral So it took me between 25 and 30 minutes really heavily focusing on grammar However, I feel like it was worth it for me to hone in and do One teacher intensive program like grammar because brielle enjoys writing And by her learning like all of these different parts of speech and grammar really really well this year I noticed a big improvement within her writing. So i'm happy we took that the time and we utilized rotten staff So brie actually did all of her written practice in these composition notebooks. She utilized using Different color pens and things like that. So she really Like doing it with different color pens. So, um, we also utilized the the worksheets right here And these were like optional. We didn't have to use these However, if it was any type of skill Brielle needed to master or work on a little bit more we would pull out the worksheets and um Sometimes when I pulled out the worksheets, she was kind of like, ah the worksheets, but But in the end it was worth it for her to get that extra practice when she needed it So this writing staff also has the test booklet, which is right here And the test booklet just allowed me to be able to see if she really honed in or mastered The specific topics within grammar and it just was just basic to the point Writing staff is a really affordable curriculum I wanted to highlight and show you guys one of her writing assignments that she did Which was a book report on on the banks of plum creek and brie did an awesome job She was only really supposed to write three paragraphs But she ended up writing five paragraphs as you guys can see and this right here is her rough draft So after she did her first draft I went over it with all the edits and then she did her final draft And she did a really awesome job on her book report. So you guys that is rodin staff. So brie, what did you think about rodin staff? I liked rodin staff. It it was um, I liked how it um build it up on each other and the lessons weren't just um Just doing this doing verbs one day then add to the next okay how to stack that So brielle was pretty much saying she liked how it was mastery And it just went over one part of speech at a time and it wasn't expecting her to know Nouns and verbs and adjectives all within the same day It just really took its time building upon each other and I really feel like this helped her a lot when it came to grammar So rodin staff and um fix it grammar you guys. They're very very good both very thorough programs I really don't feel like you need both of them. However, we just chose to do two grammar programs this year Okay, you guys the next program we did was 180 days of spelling and word study And we started 180 days of spelling and word study in our second semester and brielle She really enjoyed this program again. It's just a simple thorough spelling program We used ebb and more spelling our first semester and it went very well too One thing I will say is that 180 days it gave her a more variety of activities And I feel like it was a little bit more challenging for her and she really really enjoyed it So brie, what did you think about 180 days of spelling and word study? I liked it um because it had the um ones where you could do cursive and where you could um change the questions into sentences And it is a variety of different things different things that you could um do so it wouldn't be boring Okay, so she liked this one. I also had her fill out in her composition book Each of the days I had her fill out the vocabulary words So she was able to do the fill in the blanks a lot easier because each day she would define five words and at the end of the day She will have all 20 of her uh spelling words defined So this actually is not just a spelling program, but it's a vocabulary study as well So we really really enjoyed these okay you guys So we actually did two science curriculums this year We actually did the good and the beautiful mammals curriculum in our first semester So i'm gonna have brielle show you her science notebook that she did So um after each lesson of um after each lesson of the mammals unit Brielle she would just put her vocabulary words inside of this um Composition notebook and she would journal it. Um one thing I will say is I already have a review video on my channel about The good and beautiful science units. I like these units. However for me This was just too experimental heavy for me to be able to do this with both of my uh with um Brielle and also having my two toddlers. This was just too much for me. This will be great for family style I really feel like we kind of put off science a lot because I knew it was going to take more of me And I already had other teacher intensive. Um What is it teacher intensive subjects, but overall uh this science program? It was pretty good and I would recommend it to uh family style learning But if you are just like me you have like one school age kid and two toddlers I really wouldn't recommend these units for you to use Um, but other than that, I mean it was okay. Uh, I didn't mind it. So brie. What did you think about the science unit? I liked it and um, it was really fun to um, like cut out all the things and um Add the pictures and to like make the little puzzles and things like that But it was also fun learning the information about each animal too in their classification So you did like it. So yeah, so as you guys can see we didn't finish off the unit What lesson is this? So we the bats So we only got to about lesson 11. So we didn't finish the last three of this, but overall, um, these These science units, I mean, they're okay. Uh, but like I said, I would really recommend these for uh family style learning Not necessarily for someone in my case with just one kiddo because it is a very heavy prep and very heavy teacher intensive Oh, I forgot to show your uh painting your water painting you did when you did the marsicles and she really enjoyed this one So it was it was overall pretty good. Now the science curriculum that brielle absolutely love was god's design for life We actually did the human body and we did the world of um Animals so we did in total three sciences this year. Um after I show you guys like her, um, What is it after I show you guys her science notebook? We're gonna show you guys her big project that she did for um the Science unit in the human body. So this right here is actually brielle science notebook and She utilized this notebook all throughout when she did the world of mammals And also too when we went over the human body as you guys can see We kind of really enjoy doing like these interactive notebooks and she really enjoyed this now one thing I will say about god's design is that I really didn't like the teachers manual that came with it. I really like going on teachers pay teachers and grabbing these uh really cool printables to be able to use And uh brielle really enjoyed these one thing I will say is that um, I really found that the human body is such a simple Unit I really kind of felt like I could have did it without the Using god's design. I really felt like I could have just did this one on my own We watched a lot of magic school bus videos and um, yeah I really enjoyed all these interactive pages that I found on teachers pay teachers.  So brie What was your favorite science? the human body Or I should say the life science life science. So she said god's design for life was her favorite This is one of the first activities that she had to do god make me special And I really think she did a good self illustration on that and this is another printable from the um What is it from teachers pay teachers that went along when we went over the brand Okay, brie. You want to show them your first project you did the big one? This is the behavior and interesting facts Or like you yeah, so each of the mammals that brielle did She actually it actually took her like over a week to do each one of these little fan decks Where she had to write their uh their animal their class their classification She colored in the habitat and where they were uh found at of course they all were found in africa This was the african mammals Unit but she also wrote about their diet their life cycle their behavior And the interesting facts and this was just a way for me to do a mammals project Because we wasn't really consistent with the mammals unit. This was a way for her to still to be able to Have fun diving in deep into like all of these african mammals So brielle like did an awesome job on this display board and she actually Did a presentation for our family during christmas and this right here is um, no, no, thanksgiving So on thanksgiving she did a presentation and this right here is her Presentation that she read to everyone. So she did an awesome job on this african mammals project in the first semester Okay, so this is brielle's human body project. She's gonna show you so this is actually brielle I actually laid her out on this. Uh, what is it this, uh It's a um Parcel paper. Yes parcel paper This is her imprint and what she did was we went on teachers pay teachers and she was able to Put in the different body parts and label some of them on This parcel paper and she did an awesome job and under each of them It has like a flap where she had to like Write out what each of the body part did and their systems and it's kind of cool like how this uh one All works out. So it's really really cool. She did an awesome job on this, uh Human body poster and she really enjoyed it. So after we finished each one of the Like the nervous system and circulatory system. She will come and add it to her like big projects So this one was a really fun one that we finished off this homeschooling year So brie, which one was your favorite project the mammals or the human body? Yeah, you did work on it Yeah, you did work on this one longer. She actually uh had a limited time on this one because we were ready to start our second semester So at the end she had to like wrap this one up But this one she had all second semester to work on her human body one. So she really really enjoyed it Okay, you guys for history. We did a lot of stuff for history, but our main history was amazing africa So we utilized amazing africa, which is a heritage pack from amble or nail johnson I actually have a separate video on my channel going over in depth of our review of amazing africa But we really enjoyed it We went over 26 picture books in all 55 countries within africa and this is like the main reference book So brie go ahead and show them your um writing notebook that you did Yeah, so this is all of the countries that brielle ended up writing about and I really utilize History as another writing opportunity for brielle because again, she really enjoys writing So as we went over each of the main countries within africa She wrote a paragraph about it and as you guys are going to be able to see as she gets closer to the end brielle really is like starting to write really full paragraphs She is writing like three paragraphs towards the end So we really really enjoyed doing this africa continent study and this was a part of our geography slash history study But I do have a whole separate video of our full review on amazing africa So brie your notebook looks amazing So, yeah, so that was amazing africa heritage pack now for uh, martin luther king day We actually did this uh, what is it this free pack from the walk-off way? And it was a really cool pack where we did a week study on Who was martin luther king brielle was able to do a timeline on his life? And she actually did some copy work within her packet She did a watercolor on a dr martin luther king that week We actually did some geography and she also wrote a really really good paper on dr martin luther king So, uh, she really really enjoyed doing this, uh unit of learning about dr martin luther king And again, we spent a whole week doing this one and she did an awesome job on all of these colors So this again was a free unit from um, jessica from the walled off way And these were the two books that we read who was martin luther king and the story of martin luther king Now for a black history month. We had a really really fun time with black history mom This is just a few of the main books that we use We use little leaders both women in history and we also use little leaders exceptional um men in black history and brielle She actually had an opportunity to write some bibliographies on the people that stood out most to her One was uh, dr. Charles r drew. She did a bibliography on him. She did a bibliography on kathryn johnson She also did a bibliography on betsy Coleman Uh, and then she also did uh, her last big bibliography was on mitzy copeland So these were the people that stood out most to her these right here that brielle is showing you It's just like her rough drafts and all the practice that she had to do to get up to her final draft on her work And then these are some coloring pages that we used from puzzle huddle.com. They actually had some free pages So when we were going over uh all of the people within black history the people that really stood out to her She actually colored some pictures about them. So we really really enjoyed black history month And i'm happy we carved out that time to be able to learn about all these amazing people within black history. So um, yeah So brie, what did you think about black history mom? I liked it because it's because we got to learn about each black person having an impact in america Yeah, yeah, so it was really fun for her to do this black history study. So um, yeah, thank you guys so much for watching today's video I really hope you enjoy seeing all the things brielle and we got up to this homeschooling year I'm so so so proud of brielle. She really did an awesome job And I really hope in today's video is not like i'm really bragging on my baby girl I kind of am but I'm really really proud of her. I'm proud of everything we accomplished. I really did not believe We were going to have such a successful homeschooling year because we really started off this homeschooling year Really really rocky. However, we're so excited to start our third year homeschooling because I really feel like we know What we want. We know our groove and hopefully we have a good third year of Homeschooling. So you guys, thank you so much for watching today's video I really hope you enjoy and I look forward to seeing everybody. Am I next one? Bye You


the seven last words of Christ. These seven pronouncements embody the whole of the Gospel. Let's get into the first word. Father, forgive them for they know not what they do. It exemplifies to us both this quality of mercy and forgiveness, which was so important in Christ's teaching. If someone hits you on one cheek, turn the other. How many times must I forgive the person who offends me? Not seven, but seven times seven. You'll be able to use this saying as a powerful shield against any insults which may be directed against you and any aspersions cast upon you. The divine spouse prayed for those who killed him. Will you not pray for those who insult and criticize you? So as Bonaventure, our spiritual master telling us, hey look, you should be able to forgive people who do these little insults against you when Christ could forgive the very people who were crucifying him. The second word, amen, I say to thee today, thou shalt be with me in paradise. This is a scene which we encounter only in the Gospel of Luke, interestingly enough, of the repentant thief who according to tradition is known as St. Dismas. This thief reprimands the one who is mocking him and he says, have you no fear of God, seeing that thou art under the same condemnation and we are condemned justice.  So this promise of heaven given to this last minute repentance. Who else do we know that Jesus looked to him and said, you're gonna be in paradise with me today? Only this guy. I think it's a wonderful lesson to each one of us. Whatever situation we're in, we just need to look at Jesus say, Lord, remember me when you come into your kingdom. The third word, and maybe my favorite, woman, behold thy son. And then he says to John, behold thy mother. These words are the most touching and profound, I think, in the whole of John's passion narrative. We see that Jesus, even though he was in agony himself, in physical agony, looked down with infinite love upon his blessed mother and upon the beloved disciple, John. And this beloved disciple, John actually represents not only the apostle himself, but every faithful Christian disciple.  I see the man of Bonaventure, our spiritual master, kind of coming through the page here. I marvel that she herself did not succumb to death. So great were the waves of anguish, which engulfed her. He seemed to really tap into what Mary must have been feeling at the foot of the cross. Yes, Bonaventure had this immense love for the Blessed Virgin, and this comes through so powerfully here. The fourth word of Christ. Oh, yes. My God, my God, why hast thou forsaken me? This is perhaps the most confusing. It is, it is. Of the words on the cross. And it's something which, you know, as a priest, I'm very frequently asked about, people say, you know, why did he say that? Was he really abandoned? Surely he knew that he wasn't abandoned. And Bonaventure offers this wonderful explanation. He shows himself united with the suffering church in doing this. And so often people feel themselves abandoned by God. So this question is uttered as the voice of the suffering multitude. So it's an outpouring not only for his own agony, but for the agony of all broken hearts, all crushed spirits throughout the world. It's really almost a divine sense of empathy. It is, it is, it is, yeah. The fifth word, I thirst. I thirst. This thirst is, is expressing this kind of infinite desire, this desire and what's it for? It's not just for physical drink, but a desire for the salvation of every soul there is. You know, Mother Teresa had put in all of the chapels, you know, all the houses that she had for her nuns, a crucifix, but then right next to it, I thirst. Yeah. And I think the reason she did that was to remind us of the, those who they were there to serve. Everyone's thirsting. But Christ is, is thirsting on their behalf, but most importantly, he's thirsting for our own conversion. To see the hunger and the thirst of Christ in the hunger and thirst of our fellow human beings, that whenever someone calls a potos for help, it's actually Christ who's calling a potos for help. The sixth word, it is consummated. The Dewey Reems translation, which is Tan's preferred translation, uses the word, it is consummated. Whereas other translation, RSV, NAB, they say it is finished or it's over, it's ended. It's a very different connotation to say it is finished versus it is consummated. So actually Bonaventure expresses pretty fully what consummation here means. He does, he does. And yeah, this consummation means this bringing something to perfection, to completion, to fulfillment. Thus it was in the perfect and life-giving sacrifice of the Son of God, all the ancient sacrifices and rites of the Old Covenant are brought to their single completion. So it's like he has achieved what he said, he's achieved his mission, the salvation of the world. So yeah. It's a beautiful notion, you know? Yes, yes, which is so much better than it is ended. Yeah. It's finished. Yeah, absolutely. It is, it's just begun. And the seventh word, Father, into thy hands, I commend my spirit. It's just interesting that Bonaventure's zoning in here that he said it in a great voice. He essentially yelled it from across. His very last thing he said, he bellowed out for all the world to hear. Most people when they're about to die, they could barely utter any words and the words they say are whispered or barely audible. But Christ here displays his divinity by showing that he's still capable of crying out in this great voice. He says, just as a victorious warrior cries out when he has conquered his foes or put them to flight, even so did Jesus cry out strongly when he had defeated death and sin. I mean, that's a victorious warrior. Yeah. Right there hanging on the cross as the sacrificial lamb. That's a powerful concept. This is, this is, it's magnificent. You know what I, as I said, Connor, I hadn't imagined it in that way ever before. Me neither. But it really does shed a great light upon this. You know, this commending his spirit into the hands of his father isn't just a surrender. This is a cry of victory. He's finished his mission and now he's just making his journey homeward.


and share the tables. So let me look at this one. The one with four digits, okay, that's correct. So welcome to the final exam prep before a day before you write. So the if before you write your exam out of the way, your exam split into two sections. Session number one and session two. Session one, like with the assignment where you had assignment one concentrating on a couple of questions and chapters and assignment two looking at different chapters. You will also do the same with your exam. It's split into two so that it gives you enough time to also go for a toilet break or a breather or go from, I think nine o'clock or eight o'clock. I can't even remember, I think from nine o'clock until one o'clock. So you can take your exam any time between those time. So your time will close or your exam will close off after one o'clock. So what happens when you start your exam paper? Please check first your load sharing schedule. We know that Escom these days is back with black out. So please check that that you don't have any load sharing. If you have load sharing during that period between nine and 11, look at the times pace yourself because one session it's about 75 minutes. So it means if it's one hour 15, one hour 25 minutes or one hour 30 minutes, something like that because it's 75 minutes, one hour 45 or something like that 15 minutes.  Wait for the load sharing and then when the load sharing is done start another paper. So you can start your exam like I said any time between nine and one. So you can even if there is no load sharing, you can start your exam by 12 o'clock, but make sure that you not by 12 o'clock because then you will be late because you only have one hour. So you need to make sure that by 12 o'clock you already have started at least one of the sessions. The other thing you can start any session anyway and how you want because there are two independent sessions. One does not influence the other one. So you can start with session number two and get over done with it because it's got questions that or chapters that you feel you are comfortable with or you can start with session number one. The way you start your sessions, it's up to you. OK, number two, please make sure that it's an open book. Open book means you can bring any material, anything you want. So there's no need for me to even skinner and say, oh, don't tell anybody that. So it's an open book. It means you can bring your study guide. You can bring your question papers, your past question paper, your mock exam papers, all those things. But be mindful that the more you go search for things, it might take more time away from doing the actual exam. What I will suggest you do today after we've done with this, take a breather and go back and summarize information, put things like make yourself a summary page where you know that study unit one, we cover one, two, three, four, five and have this and this and this. These are the formulas that are required for answering this kind of a question. Make notes for yourself and have that as your point of reference before you can go to your study guide to any other page in through the textbook and so forth. If you have that as one of your input, it will save you a whole lot of time because those are notes that you made.  Number three, also tables, your lecturer set in that tutorial letter. You need to use your tables that were given in your tutorial letter or your study or some way, I can't even remember now which one, the tutorial letter one to one. If you have tables, use those. Otherwise, there is a documentation that we have been using during our classes that I shared with you. It's got formulas and also it's got tables and we're going to use it today as well. Use that as your reference tables for tables so that you don't have to use a different table with three decimals or two decimals so that you standardize your things. I use the one with four decimals. That is all in terms of your exam. There's nothing more. There's nothing less. The only thing that you need to do during your exam is just take a breath, relax, and tell yourself, I can do this. Do not panic. Do not go into a panic mode when you can answer question number one. Say, ah, that's easy. Which whatever goes goes and then you answer your question paper. And that's all from me. So now let's go into it. Let's start looking at the mock exam paper. I thought we can look at any other exam paper, but we're going to just look at the mock exam paper. Guest, you can unmute. Good day everyone. It's just going back to the exam itself. Will it be a linear exam where you have to answer a question before you move to the next one? Yeah. Can you hear me? Yes. Yes. I think I got lost like a network. Yes, I do. Wow. It's been challenging. Yes. Okay. Can you repeat your question or I didn't hear that? So I was asking about the exam itself. That will it be a linear exam where if you skip a question, you can't go back? I think so. The same format as your assignment. So it means once you answer the question, you just move on the same way. So yeah, it will be a linear. You can't go back to the once you skip two, you need to answer that question. Okay. Thank you. No problem. Okay. Are you able to see my screen? Yes. Okay. So no problem. And then we can touch. With question number one, without wasting any time, because we only have two hours to do the rest, to do all of them. Which one of the following statement is incorrect with regard to a statistic? So I assume at this point you all have read, you all have revised. Is it A, B, C, or D, or E? Statistic. I'm not sure if you are using the chat, if you are using the chat, also using the chat. Somebody also posted the tables on there. So you can also, if you don't have a copy of the tables, you can use that. If you're using the chat to communicate with me, I will have to join on my phone as well, so I can see the chat. I think the answer is B. So we have B, and on the chat we have D, B, C. Okay. So a statistic, sorry. I was still busy trying to get to my, let's give me a sec, to my chat. Okay. So you must also remember what a statistic is. A statistic is a measure that comes from a sample, right? Those are measures that comes from a sample. A says a statistic is a summary measure calculated from a sample. We're looking for the incorrect one, and that is correct. Number B says a statistic is not an estimate of a population. It says not, because we know that a sample statistic, we can use it as a point estimate to estimate the value of a parameter, and that we use it in the confidence interval. Remember that? So for the fact that they say not, that makes that statement not correct, because we know that a statistic is, it is an estimate of a population parameter. C says a statistic represents the property of a sample that is correct. A sample statistic or a sample mean, which is your X bar, is a statistic. It is a measure that we calculate from the sample. A sample standard deviation is also a statistic, which is your S. Okay. So the only incorrect answer here is B. So you need to remember that. From a population, we get a parameter. From a sample, we get a statistic. Question number two, information on the following variable is gathered amid COVID global pandemic. Which one of the following statement is incorrect? A, the medical cost of each patient in rent is a quantitative continuous variable. Remember? Yeah, we're talking about variables. So you need to remember that quantitative variables can be counted or measured. If they are counted, they are continuous. Sorry, if they are counted, they are discrete. If they are measured, they are continuous. So you need to remember that. We also have qualitative variables, which are variables that you can place in two categories. So now it says the medical cost. The most important thing is that the medical cost of each patient in rent. That's the statement you need to evaluate. Whether is it a quantitative or is it a qualitative? And we're looking for the incorrect one. The name on the list of the province affected by COVID-19 is a qualitative nominal. Name or list of provinces, that is what you need to evaluate. Is it qualitative or quantitative? And because also they mentioned nominal, you need to also remember them. For qualitative, the scales of measurement or levels of measurement, we have nominal where there is no order or preference or levels. And we also have what we call an ordinal where there is order or rank. So you need to check whether that statement, is it nominal? The severity of a symptom, whether it's mild, moderate or severe, is a qualitative nominal variable, like I explained. So you just need to look at actually what is inside the bracket. It's most important to evaluate. Common COVID-19 symptoms such as cough, fever, tiredness, shortness of breath is a qualitative nominal. Also the same under there. Sorry, are you asking a question? You just need to check the information in the bracket. It will give you guidance in terms of how to answer that question. E, the number of confirmed COVID-19 cases is a quantitative discrete variable. A, B, C, D or E. Which one is incorrect? I say it's C because isn't it supposed to be ordinal variable instead of nominal? You say it is C. Yes. C because it's supposed to be ordinal, not nominal. Yes. C because that information there, it should be, the answer here, that should be ordinal. The total number of COVID-19 confirmed cases. Can I ask a question? Yes. On that question that we just passed, number A is just, I'm a bit confused because I thought it was A. Is it, can we count, can we count that number A? What is it saying? Is it a medical cost? Yeah. So it's not discrete, not continuous because, can we measure, sorry, we can count but not measure? No. You can't count. Okay. So what do you need to also remember? Yes. What you also need to remember is, in terms of continuous, it is those questions that you can ask by how much? How much and discrete you can ask, answer by how many? So that should give you a guidance. Continuous, much. I hope my continuous, I wrote it correctly. Conti, it's got another U somewhere that I'm missing. Continuous and discrete, we answer. So those should be your guidance in terms of how to determine also which one is a continuous and which one is a discrete. Right? Moving on to the next one. So we are given a frequency table with the provincial breakdown. We need to answer the following question and choose which one is incorrect. A says the percentage frequency of umpumalanga. How do we calculate the percentage frequency by taking the value? So this 37 divided by the total number multiplied by 100. So that will be your percentage frequency. You say 37 divided by 15, 5, 1, 5, multiply the answer by 100. That will give you a percentage frequency. So you need to do the percentage frequency from umalanga, which is 71. The frequency of notary and cape, which is this are your frequency. The actual values they gave you, which they say the number of. They can also put it as a count. Those are your frequencies. So if you look at notary and cape, which is notary and cape is the first one. Is the frequency of notary and cape 37. We're looking for the incorrect one. Always bear that in mind. The relative frequency of how thing. So relative frequency. I'm going to write it this site relative frequency is the same as your percentage frequency, but relative frequency. So let's say for notary and cape, it will be 37 divide by 15, 5, 1, 5. That is your relative frequency.  You take that value divide by the total that will give you your relative frequency. The frequency of Northwest. So remember frequency is that column. So you go to Northwest and you look at the frequency of Northwest is that the frequency of Northwest. The relative frequency of Eastern Cape. You go Eastern Cape. You take the value of Eastern Cape, which is one nine. 36 divide by 1, 5, 5, 1, 5. And that will give you your relative frequency. So the difference between relative frequency and frequency percentage percentage is your relative frequency multiplied by a hundred. If you look at the notes, we also have. An example of that a b c d. D. D is the incorrect statement because the frequency of Northwest is equals to 70. So that should be 70.  If you want to say anything, you just let me know. Okay, given the data below, it shows the stem and leaf plot of daily COVID-19 cases during the second week of the national or the nationwide lockdown. Now we need to use this information to answer question number three to question five. You must always remember with your stem and leaf plot, you need to know how to read your stem and leaf plot. Remember the values you see on the stem and leaf. The first digit before the line, this are what you call the stem and this are your leave. There is one stem and many leaves. So this value is not one, but that is 31 and this value is 43 and that is 63 and so forth. 63 and so forth until you get to 96. So that's how you read this table. So in order for you to answer the questions, you need to decipher this table or this stem and leaf plot by doing it that way. So I'm going to give you some time to think about which one is correct. So remember a symmetric means the mean is equals to the median. That's symmetric. The mode refers to the most frequent or the number that appears more than the other numbers. So it means the number that is repeating more than the other numbers. So for example, if they had another zero there and another zero there, then it means 70 repeats more than the other numbers. So that's what we are referring to there. The range is your highest value minus your lowest value. The mean is the sum of all your values divided by how many they are. The median, you can go and find the median position by using n plus 1 divided by 2. And then using that to go find your median. I'm going to give you some time just to work through it. I will be back. Have you all thought about it? Have you got your answer? A, B, C, D, O, E. A, A, A. The data is not symmetric. The other thing you can also use to identify, symmetric will mean that probably this line would have been somewhere in the middle. But that is also not in the middle. So that your stem and leaf plot would look like normally distributed like that. The moment you can see that it has a tail 2. This one. We can draw a normal distribution like that. You can see that the tail is to the left. So A is the incorrect statement. The next question also asks about the same stem and leaf plot, but now we need to do the quartiles. Remember, quartile 3, we use 3 times n plus 1. Divide by 4. Quartile 2, n plus 1, divide by 2. And quartile 1, position. Remember, these are all positions. Quartile 1, position, we use n plus 1, divide by 4. Or you can use 75%. So this is 75% times n plus 1. This is 50% times n plus 1.  You can use the percentile or you can use the quartile formula. This we will find the position. So you must read your question correctly and carefully. Because in your question it says the value. Let's see. Interquartile and value, yes. It's your screen still shift because I can't see you. You don't hear me. No, I can't see you. You can't see me. Yes. I can't see you. Yeah, I'm good. Oh my goodness. I can't see the screen. I can't see. I think it's back now because I also couldn't see, but it's back. I can see. Oh. All right. So this is value position, position interquartile range. So this is to find the position. The answer you get when you find the position and the answer is 0.5. Then remember to take the average of the two values that both of them are located between. If the answer here is 1.5, you go find the average between the value between 31 and 43.  That is if the answer is 1.5. So you take an average if the value is 0.5. Now, if the value you go into round it down, like we do with the normal rounding up and rounding down. So that will round down. So if the answer was 1.25, you just round it down to 1. So then it will be 31. So if the answer is 0.75, then we round up. So if it's 1.75, therefore our quartile value will be on position 2. So you just need to remember all that when you answer the quartiles. I don't want to remove all of them. I only want to remove these ones that I just wrote. So you need to go and find the position for quartile 3 by using that position value. You need to go find. You've gone Miss Lizzie. Position, sorry, calculated the position, then you can go find the value. Inter quartile range is your Q3 value minus your Q1 value. That's the incorrect one. Time to work through it if you haven't. Your communication is just breaking up every now and then. I think my network is bad. Hello. I can still hear you. I think it's maybe Lizzie. Yeah, I think so too. OK, just making sure. Am I now audible? Yes, yes, yes. Yes, you are. All right. OK, so let's. Do you have an answer or are you still working out? The answer is D. The answer is D. So what is the value of Quartile 3? It's actually 46. Is 46. Inter quartile range is 46. Inter quartile range is 46. OK. So the answer here is D. Sorry, can I just ask a question? Yes, you can. So you're doing the inter quartile range. It's based on the position. It's based on the value, not the position. Yes. OK. Yes. And then how do you find like the value? Because I'm having struggling. The position. OK. Not the value. I think. No, the position. Yeah. OK, so let's let's find the position. So you did say three times N plus one. Divide by four. You say three times seven plus one. Divide by four, which is eight times three. Divide by four. What is the answer you get there? Six. Six. Is it six? Yes, it's six. Yeah. Then you go count. So don't count this values yet. Just count the values, the leaves. So say one, two, three, four, five. But you must also count this value because it's also a position. Six. So then when you read this, you say 89. So the value is 89. OK. OK. Because this is a stem and leaf plot. Remember? Like we did here. I said when you read this value, you say 31. Like we deciphered it. Yeah. This is the one for the three. So this is 89. It's on position. Six. Don't come from here and then start from this side and go there. Start from the smallest value and go up to the highest values. OK. So that is how we found quarter three. And you also need to find the quarter four value. So if there's two values are correct. Therefore, this was 89 minus 43, which is 46. Thank you. That's why it makes that. OK. Moving on to the next one. Consider a stem and leaf plot. Also, we still on the stem and leaf plot. Now on this one, you will have to decipher this information and capture the information and calculate the values. You will need to calculate the standard deviation because they say the mean is 67.43. What is the coefficient of variation? So a coefficient of variation is your standard deviation divided by the mean multiplied by 100. You are given the mean, but you are not given the standard deviation. So you need to go and calculate the standard deviation. Now, you can either use your calculator and take your calculator to state mode. I hope by now you know how to do that. Or otherwise you have to use your formula, which is the square root of your variance, which is the sum of your observation minus the mean squared divided by n minus 1. So if you use the formula, since I don't have my calculator and my trial version of my calculator is finished, so I don't have money to buy. So you just need to say the mean they gave you. So you will say 61 minus 67.43. And then you'll say squared plus. And you go to the next one. 43 minus 67.43 squared plus. Plus until you get to 96 minus 67.43 squared divided by. Oh, I must not forget the square root. Divide by 7, 7 minus 1. Otherwise you can use an Excel if you don't, if you don't have a calculator, since we always use Excel to assist in the exam as well, you can also use your Excel. But I will prefer you to use your calculator to save time because if you have created the templates for yourselves and then you can use them. And if you're going to use templates, you need to know how to operate the templates because then sometimes they are not straight forward. There are things that you need to adjust when you use your templates. Please kindly share how to do it on a calculator. What calculator do you have? I have a Casio scientific calculator. Okay. On your Casio calculator, you go to mode and then you will press the number that corresponds to what you see. G-C-S-T-A-T stat. Yes. What number is that? It's two. So you will press mode and then press two and what else do you see? There should be one that says one var. Yeah, one var. It's number one. You press that number which is one and you will have a table and a table that will have an X column. Sometimes the table will have a frequency there. You can just ignore the frequency. We're only looking for the X. Now, you're going to capture the value by saying 31 equal. When you press 31 equal, oh, sorry. When you press 31 equal, it will put 31 there and then you go to the next one for the 3 equal. It will place it on the table. 63 equal. It will put there and you complete the whole table. 80 equal, 89 equal, 96 equal. Do all of them until you get seven of them on there. Once you have all of them. OK, up to 96 is. OK, now you are ready to calculate your state functions. So it's very difficult to use a pen on. So now you need to press the AC button which is just to get your calculator. You will press that. OK, let's go back to normal. Now you need to press shift. OK. And then you will need to press button number one. On button number one, there is an STAT. Look at your calculator if it has that. On button number one. Yes, that's the button you press. Now you'll need to tell me what you see on your screen. I'm seeing one saying type two data, three, some four variants and five minutes. The one that says var, that's one that's the one that we are looking for. So you will press four for var. And you will see there will be in the mean. You need to look for the one that has an X. An S and an X. That looks like that. That is the standard deviation that we're going to be using. So on your calculator. You just press the number that corresponds with that. Give me that number. It's four. Divide by six seven point four three. Multiply by a hundred. Sorry, you said the number that I'm getting the SX number is twenty three point seven six. Okay. Twenty three point seven six. Yes, that's the one that I'm looking for. So that's how it is. Twenty three point seven seven divide by sixty seven point four three multiplied equal. So say twenty three point seven seven. Divide by sixty seven point four three. Equal multiplied by a hundred. Equal. What is the answer? Eighty five point two five. Thank you. No worries. Anyone who wants to take up? Sorry, Lizzie. Can I just ask you to repeat? What do we press after we have the SX that says twenty three point seven six? What do we do after that? No, that's the answer we're looking for. Remember your S. S is the SX on your calculator. And you just take that value and you substitute. Otherwise, since because I'm not sure what your X by is when you calculate on using your calculator. You can say where are you at now? Let me remove all this weakings. You can say after you can say shift one. Four. No, is it four? Yes. Four and four again. And say divide by. One. Four. What is the value that corresponds to X bar? Is it two or three? I think it's two. Quickly check. Go shift one four. And tell me what is the value that you see that corresponds to X bar? True. Is it two? And then press equal. And then once you have that multiplied by a hundred and then say equal, you should get the answer that we're getting. So this is from the calculator. So you will do it that way. I'm sorry, Miss Lizzie. Yep. I can't see the chats on my side because I joined with a guest account, but I'm getting the standard deviation of 22.01. I'm not sure if I'm the only one. Which, which, what did you use to calculate? I use the spreadsheet. You use the spreadsheet. Okay. So now I'm going to use the spreadsheet as well. So let me just do that because I've got all the values. Edit. These labels, it's grouped by column. Maybe I should, I should be sharing my screen. Yeah, Miss Lizzie, I was about to tell you. Just give me a sec. Okay. So on your Excel spreadsheet, I just need to double check if my values are correct. There are seven of them. Okay. So on your spreadsheet, you can have all your values. And depending on the type of a spreadsheet that you have. On my one, I do have an editing called the data analysis. I think when we did the regression as well, I showed you how to, to get that in. So by going to the file option, file options, and then you go to addings. And then you add your Excel, Excel editing. Okay. So it's an Excel editing and you go to the analysis tool pack and say, okay. And you select those analysis tool packs. You need to make sure you can select one, but I selected both of them. And then you click, okay. Then you need to restart your Excel sheet. And once you do that, when you go back to your Excel, the data analysis panel will appear under the data menu bar. You will have this section called the data analysis. So under the data analysis, you will capture your data.  Opens up this menu bar and you look on the menu bar. You will look for descriptive statistic. If we were doing regression line, the regression model will be there. But we're not interested in that. We're looking at descriptive statistic and you press okay. You need to put in your input values. Let me remove all these values that I have already. You go to your input value. You make sure that your cancer is flicking on the bar. Then you go and select the values. So if I select from X. I must also remember if I select from the label. I need to come and tick this. That says labels in my first row. So that it knows that I have selected labels in my first row. And I also need to tick one of them. Sometimes your data can be written in that manner. In the row manner starting from 31 from these columns. And my one is grouped under columns. So if you have any pop-ups open, we won't see them. You're clicking away. We don't see anything. You need to share your desktop. I don't want to share my desktop. You can hide all the stuff we don't want us to see. I'm fortunate that I made work. Okay, so you go to the file. Sorry. To add the data panel. File options. You go add-ins. Analysis tool pack. You click on the go. And you tick both of those. Analysis tool pack. And you click OK. Then you restart your Excel. You go out. You close this Excel and you open it again. Once you open the new Excel sheet, you come in. You capture the information as you want it. Sometimes you can take the same information and capture it in that manner. It doesn't matter how you've captured it. So you can do it that way or you can do it that way. And then you don't have to do anything. You go to the data panel. Data analysis. And you select descriptive statistic. Click OK. You're going to choose the values that you are using, including the label if you want. And you need to make sure that you tick the labels in the first row. You also need to tick where it says group by. So mine is grouped by column. If it's grouped by rows, then that will be grouped by rows. So we're doing the one that is grouped by columns. You also need to select the input output range. Also make sure that your line flicks inside the empty column there. And then you select any way where you want the output to be. You can also select the new worksheet or the new workbook. It will open a new one. A new worksheet, it will open another worksheet. A new workbook, it will open another Excel book. So I want my data and my report to be on the same page. So I just select any way inside this Excel sheet so that it creates where it will create the output. You also need to select the summary statistic so that we can have all the summary statistic. And then when you press OK, and there is your output. So this one is the one that I did earlier. You can just delete that. And you have your data. So you need to be very careful when you use this template as well. You will get two, you will get a standard deviation.  So if I look at what we got, what did we say? We got 27, 23 points. So our CV, the previous one, because I removed all the values that I had, you had 23.77. Yes. Over the mean of 67.43. 43. Yeah. So if you look at the Excel output as well, and that is what we get, maybe I should go this way, 23.77. And the mean they gave us, but you can also get it from there as well. So that is how you can use an Excel, but let's not dwell too much on that. Otherwise you can use your calculator. You can use the formulas or you can even calculate it manually by applying the same thing. So by saying, we know that that is 31 minus 67.343 squared. And you just do the square. And you do the same. What am I missing? Oh, my comma. My comma needs to be a decimal point. And you can do the rest, the same as the rest. Sorry, my bad. I needed to change it to that. And we can have the sum, which will just be, I need to make it bigger so I can get my summation. Or to sum, that is my total. And I can take that total and calculate my deviation. I just taking the square root sqrt of this value divided by 7 minus 1. Or I could even set count minus 1. And that is my standard deviation weight. They didn't calculate correctly. So what am I missing? Double check something. You need to put the 7 minus 1 in brackets. Oh, yeah, you are right. That's the same mistake that I did. I noticed. Yes. That's correct. They need to be two closing brackets. Okay. And that's, you can see that I get the same answer as that. So this is the summation. If I put it that way. Okay, so you can use whatever, whatever you find at your disposal to help you. But don't dwell too much on technology and this and that. And then you can see that how long it took us. So you just need to make sure that you have prepared to use all this, all these tools if you want to use the tools. And you need to practice. You cannot use the tool when you get to the exam. And multiply by a hundred. Which did find that that was the answer. Okay. Moving on. We are still very far from finishing. Which one of the following statement is incorrect with regards to the experiments? Just give me some few minutes. It's such a gangsta ringtone. Just picked it up now. Okay. So this one, it's almost exactly the same as what you had in your assignment question. Which one of the following statement is incorrect? We have number of permutations of three items that can be selected from eight groups. Already they told you that that is permutation number of combinations. So it means you're going to use NPR to calculate the way your N is 56 and your P is three. So you know where to find that. You must look on your calculator for that function. If it's written in orange, you're going to use the shift button. So you will press five. Sorry, Liz. Yes. I think you substituted the 56. It's the wrong number. It's not N. The N is actually the eight. Oh, 56 is the number. Yes. Oh, sorry. The whole sentence. So that will be eight. Yes, you're right. That will be eight. This is the answer that you need to get. So you'll press eight. Second function and you go find that button that corresponds to the NPR. Three and that will give you your answer. Combination same for seven item. Out of five. Five items out of seven. So that will be seven C five. And this is what we call a combination question. You also do the same seven shift or seven second function depending on what calculator you are using. And go find that NCR button and then press five. And this is just, you need to know that the definition of probability, what is a probability? And the next one in an event with a four equally likelihood event. So you just need to know what is the probability of a simple event when you have four of them. So the probability of X will be, what will be that? What will be the probability of that outcome? Number five experiment with three steps. And four outcomes possible for each step. So yeah, also you need to find the number of ways that you can get those outcomes. And we are looking for the incorrect answer. The answer is A. A. The answer is A. What do you get when you calculate the permutation? 336. In the exam, you don't have to do all of them. When you get to the answer, you just move on. You don't have time to evaluate all the responses. Next. Yes. I would, can you do B? I don't know why I got 2520. B, you will say seven. Oh, okay. Okay, sorry, I used P, sorry. Consider the following below, which is the contingency table. Now with this question, you are given this contingency table and you are given decimals. So you need to know and remember when we talk about probabilities as well. So because this is probabilities, because I can see in the question, it asks questions about probabilities. You need to remember that when the statements or when in the statement you are given whole numbers like 20, 30, 70, 120. This we call whole numbers. We call them outcomes. These are events. So it means we can use these values to calculate the probabilities. When you are given decimals like this, these are already probabilities. So we can just use those probabilities to calculate. Sometimes they can give it to you as a percentage, which we call them proportions. As percentages in probabilities, when it's in a percentage format, we say it's a proportion. When they give it to you as a percentage, it's also probabilities because you just divide that percentage by 100 to get it to a decimal. So here you are given the probabilities. You just need to use these probabilities only for any formula that you need to be calculating. So let's look at the questions given. Find the probability that a caregiver works from home and their children is securely attached. Now, with this example or this question, they actually made your life easier because they gave you this in the bracket, which is what I wanted to write. The probability of home and secure, which is the joint probability. Therefore, we know these are joint probabilities from this. These are all joint probabilities. We know that we calculate joint probabilities there and we calculate simple probabilities from here. Now, before you even start answering questions like this as well, because you will require the total, I will suggest that every time you do answer the questions on probabilities, you write the totals. So you can quickly write this total. So this will be 6.5, which will be 0.5. So this is the same as the probability of secure, which is 0.56. That's how you will use the probabilities. So you need to complete this whole table. Do that before we can start answering the questions. And once you are done, let me know what values I must put on here so that we can work from the same common table. Are you done completing the table? Yes. Okay. You mean the values? Total for home would be 0.53. And total for home would be 0.47. Yes. And for insecure it's 0.44. Okay. So now we are ready to answer the question. Probability of home and secure. Look at the table. Joint probability. So this is probability of home and secure. They say it's 0.15. We are looking for the correct statement. Is that correct? No, that's wrong. Okay. The next one, we're looking for the probability of home and secure. Now on this one, you need to do a little bit of work. You need to write the equation of probability of home and secure is equals to the probability of home plus the probability of secure minus the probability of home and secure. So what is the probability of home? You told me that it's 0.53. Plus the probability of secure, which is 0.56. And the probability of home and secure is 0.38. Minus 0.38. Is that correct? It's wrong. That is also wrong. The next one, it says find the probability of home and secure. This is conditional probability. And for conditional probability, probability of home, given that it's secure, it's given by the probability of home and secure divided by the probability of a given, which is secure. Now you just need to go and find home and secure is 0.38. Divide by probability of secure is 0.56. And that is equals to 0.67. 0.67. So therefore this one is also not correct. The last one, oh, not the last one. The second last one, the probability of secure given that home. So also here we need to go find the same thing that we did with that one. We do the probability of secure, given home is the joint probability of secure and home. Oh, why am I writing the whole sentence now? And home divided by the probability of home. So we do the same probability of secure and home is 0.38. Probability of home is 0.53. 0.72. 0.72, so the correct answer is D. The last one, they wanted to just confirm the probability of home. Probability of home is 0.53. Which means that is not correct. Okay, that is probabilities. Also going to the next one. So the next one also deals with the same information, but now we need to find the incorrect statement. What is the event? Oh, so we need to find which one, which statement here is correct. The event is secure. The event secure and insecure are complements. Is secure and insecure complements? Yes. There are complements. It's like the same as the outcome of a coin.   That's the same scenario. The event home and away are mutually exclusive. Correct. Correct because you cannot be home and be away at the same time, so they are mutually exclusive. The event home and secure are independent. Now how do I know for independent events, the probability of home given secure should be equals to the probability of home? Or the probability of secure given home should be the same as the probability of secure. You can use either one of them to test that statement. Remember you did this previously. You have the probability of secure given home and also the probability of secure given home. Secure given home and home given secure. So let's use the secure given home, which is 0,72. Secure given home is 0,72. We need to make sure that it is the same as the probability of secure. The probability of secure is 0,56. Therefore, they are not the same, so they are not independent. If they were the same, we would say this statement states that they are, let me write it here. If they are the same, we would say they are independent events. Because we know for independent events, the given probability of secure given home, home doesn't have any bearing on what happens to secure, so it will be the same as the probability of secure. The same you can do with this one, which is home and secure. What did we get? 0,56. So the probability of home given secure is 0,56. And the probability of home is 0,53. They are not the same, yes? Just a quick question. When you're doing the independent and the dependent, where it says home and secure? So that's not the mutual, not the joint probability. Do you have to use the given probability to determine if it's dependent or independent? But these are not probabilities. Yeah, they're saying events home and events secure. So this you treat them as separate. Event home and event secure are not independent. It's not a joint probability. It's not a joint event. So can't you just then just say home and the probability of the 0.53 and just secure, which is 0.5 and then put them together to say if they are dependent or not independent? Nope, you can't do that because this statement needs to be correct for them to be independent. Oh, sorry. Here it's insecure, not secure. Actually, I answered question number D because I used secure, not insecure. So on this one as well, you just need to use insecure. Sorry, my bad. So we answered D, not C. Oh, okay. Sorry. Sorry about that. I'm going to get disturbed all the time because I'm still at work. I'm still in my work time. Okay. So thanks for pointing out that, but now I've realized as well that we are discussing the third one, which is secure, home and secure. So which is this one? So this is for D. So we've done D. So you can also do the same with home insecure. You need to go and say the probability of home given insecure, insecure should be the same as the probability of home. So you need to go and calculate the probability of a given home insecure. So which is the probability of home given insecure, which will be given by the probability of a joint of home. And now this is the joint event insecure divided by the probability of insecure. And then the probability of home and insecure is 0,15 divided by the probability of insecure, which is 0,44. So now, so to answer C. So we answer C with that one. So this one answer B. So what is the probability, which is 0,15 divided by 0,44? 0,34. 0,34. Which is 0,34. So we also do the same. So that is 0,34. Is it the same S? Nope. 0,53. They are not. So they are not independent. So that is correct. That's what we are looking for. Now D, home and secure should they say, the statement says they are independent. We also did find out that they are not independent. And that's how you can only answer this question when it comes to independent. Now, when it comes to the probability, because sometimes in the exam, they might not ask you the same questions like this exactly. You need to be very, very careful when you answer conditional probabilities as well. So for example, yeah, when we were answering conditional probability of secure and home, if the statement before that, where they say the probability that they charge, if they say, given, oh, if event, secure and home are independent. If the statements start with that saying, secure and home are independent. What is the probability that the child is secure given that they are at home? You need to remember to use the independent statement. So the probability of home given secure, you need to use this. So you can use the conditional probability. You can go and calculate this conditional probability. You will have to use the one for independent. Only if they tell you that the events are independent, then you use that one. Okay, now we're moving on. Left, the basic probability. So the other thing that you also need to be aware of is because you've got 25 questions and they are split into those sections. Every chapter might have two questions in the exam. So you will get 222. Like you can see here, we have two questions from basic probabilities. Actually, we had three questions from basic probabilities because also this one is from there. But usually questions are<PHONE_NUMBER>2. Okay, so next we're moving on to the next question, which talks to probabilities. Now, looking at this question that we have, we need to remember that after the basic probability, you go into discrete probabilities. And discrete probabilities has binomial probabilities. They also have a Poisson probability and the discrete probabilities. Now, this question is your binomial probability because they gave you the probability of success or the probability, the pi probability, and they also gave you your N. Remember also the signs. These are very important, very, very important when you answer probabilities. Greater than or equal, it is at least. Less than or equal, it is at most. So you will have to answer those questions like that. Equal is exactly, exactly. So what is the probability that at least 14 branches operated? So we know what our N is. So that is very important. You need to know your N. Your N is 20. You need to know your probability of success, which is 0,35. You need to know your sign. So now we need to go to the binomial distribution table and go and find out which one of the statements are incorrect. So 14 branches at least, we go to the binomial table. Remember the binomial table as well. It has the positive and, sorry, it has the top and the bottom side of the table. Remember where the small probabilities at the top, we use the left. The big probabilities at the bottom, which are this ones at the bottom, this ones at the bottom, we use the right. So this probabilities at the bottom, they will correspond to the N values on the right and the X values there. So now looking at the question that we have, we have N of 20. So we need to go to N of 20. So that is N of 20. There is this N of 20. I will need to turn the table around now again. So you need to be very careful as well, because I can see that the values here at the top are big numbers. So I need to turn it. So it's easy if you have it printed then online as well. So if you have a copy, a hard copy of, so we can use this site. We can use this site. We need to use the top and the bottom and the left. Please kindly repeat that. How do you decide which site to use? The smaller probabilities we use the left hand side. So we need to go to 0.35. We know what our N is. 0.35, that's our pi. And we need 14, at least 14. So it means we go to 14. Very, very difficult to work with this. Am I still on the right line? Yes. You just add those three. Which is 0.0015. 0.0015, which means it's correct. Exactly 14. So exactly 14 you just use. Exactly 14, which is that value there. 0.0012, which means that is correct. The probability that all 20 branches operated. All 20 means all of them. All 20 of them operated. Which is equals to... Isn't it 1? It should be equals to 1 if all of them have operated. Did I close it? What happened now? It opened twice. Okay, so we'll toggle between the two documents now. So this is the incorrect one. It should be equals to 1. Because it's all of them. So the incorrect answer here is C. I don't have to go through all of them. Because now this one where it says most 14. Then it means you need to... From here, you need to add all of these values. Starting from there. Starting from 0.12. Or you can say 1 minus 0.03. Because that's... So you can also just say 1 minus 0.0003. It should give you the same answer. Which will be 0.09. None of the 20 branches. So none of them, which means 0. So you just go to 0. None of them is 0. Which is 0.02. And that's what you will get. Can we do one where they ask the average number of branches closed during LL5 is 19? There? When they ask for the average number of branches closed during... So when they talk about average, then they're asking you to calculate the expected value, which is the mean. So you will say N times pi. I guess probably they should be some way where we will calculate that. So let's see. Yeah. For example, it might be a question like this. Average. So you just need to remember to use the mean. But now this one is not the one that I'm looking for. This one is Poisson, sorry. This is Poisson. If we are on this one, so the average or the expected mean they will be 20 times 0.35. And they can also ask you to calculate the variance of this. So your variance, which is sigma squared will be N times pi times 1 minus N times pi times 1 minus pi. And if they ask you for the standard deviation, you just take the square root of your variance. So if they ask you for the average or the mean, you can also call this the mean, the average or the mean. And if they ask you to calculate the variance, maybe I should also write by no meow at the top. And this is your standard deviation. Okay. So the next question is on Poisson. And how do I know that it's Poisson? Statements also do assist because in they, when you read your whole sentence, you will realize that they have given you all the information that you need. Okay. So a food traffic on the number of customers entering the mall was estimated to be 20 per minute. So on average, it's 20 per minute. Assuming a food traffic is Poisson distributed, which one of the following statement is incorrect. So now with Poisson, your table is divided by the lambdas. So it means they should have given you the lambda, which we can safely say here our lambda is 20. Let's go to the C. Yes. I used the study guide. It's there on the study guide on page 96. You used it there? The study guide. Lambda for 20. I'm saying the lambda for 20, it's on page 96 of the study guide. The study guide. Yes. What does it say? I mean, the table is there on page 96. Oh, you mean the table? Okay. So what's confusing me here is that 20 is not it cannot be a lambda. It cannot be an average. So if that is an average, then it means we're going to have to calculate this manually then because this is your, if you look on your table, does your table go beyond four on your study guide? It's up to 20. It has 20. It has 20. It has 20. Okay. So then we're going to rely on you to give us that. Let me see if I do have a study guide. Maybe I can open the study guide. Just give me. And you said it's page. This one might be old. It's page 96. Just before chapter six. It's page 96. 96. Okay. Page 96. So it has, so you can make note for yourself when you go answer questions on Poisson and they is our lambda of 20. So we do have that on the study guide. Okay. So we should be able to answer this question. So going to our question, our lambda is 20. And yeah, it says, what is the probability that 19 customers will enter the mall. So this is the probability of exactly probability of X is equals to 19, which is exactly. So you just go. 19. I think this. Which is that one that will give you your answer that you are looking for. That is correct. for the incorrect one. We are always not in class, but talking to somebody, please mute yourself. The probability that 35 customer will enter, so you just need to go to 35. If you can't see your table screen. You can see my table. What happened? Oh, yeah, right. Leslie. Yeah, I just want to ask you a question. Are you African or English? I'm I'm Twana. I'm not English or any. Yes, I am Twana. Oh, OK. It sounds like you're African. Yo. Yeah. Ah, ah, yeah. Yeah. Exactly because of the swearing. Oh, yeah, but can you speak Afrikaans or not? Maybe maybe me being in Cape Town for very long time had an influence. It's very funny. OK, so I think we are back now. Everything should be visible. So let's go there. Sorry, sorry, sorry about that. Oh, gosh, 90. There we go. I think we are there. So you go at this at 20. So the first one that we looked at was 90. So the next one, it says 35 customers. So we're going to look for 35. And there are your 35 customers. And then the next question says the variance. Now with Poisson, remember.  So what is the variance? That will be correct. Then the next one says at most 35. So yeah, we need to calculate the probability that X is less than or equals to 35. So now you need to do some work. You can either choose to add all these values from 0.7, 0.120, all of them, all of them, all of them. Or you can say in order for you to find the probability of less than or equals to 35, you can say it's the same as 1 minus the probability of X greater than 85, which then it means it will be 1 minus adding up all these probabilities, 0,004 plus 0,002 plus 0,001 plus 0,001. And that will give you the probability of less than 35. Do you have an answer? 0.992. 0.9992. And this one says the value is 0.15. So that is the incorrect one. And what is the mean? Maybe I'm going to make it clear. Change. And the meaning is 20. OK, that is poison. I see that our time is almost done. We are on part 12. Unfortunately, I have to go fetch my son at school at 4 o'clock. So that is why I schedule this from 2 till 4. In fact, there is nothing wrong with you continuing to do the discussion. Sometimes someone will have to share this screen or you can work through it on your own without anyone sharing. Or you can wait for me to come back at 5 o'clock and then we continue. We shall wait. OK, so we can take a break. Shall we wait? Yeah. OK. So do we exit and then come back or we will just wait just like this? No, let's save data. Let's exit and come back after 5 o'clock. I will let you know when I'm back in the house. OK. Thank you so much. I wonder if we're going to finish the exam tomorrow. You will see. Remember there won't be this explanation. You are there and doing the work. Yes. I just have a suggestion. Can you send us the PDF? Then we work on it whilst you're still fetching your kit. I will send it. I will send it. I will send the same one that we have here. Let me save it. So this one is not the online one. That's the same one. It's the same one. It's the online one. So now you will have the PDF. All right. So when you come back. Send it. I'm going to send it on the watch. OK, so because I think we also have people who are. From other groups. Yeah, who are not from the group. My group. So I will. You guys, you will sort yourself out. I will attach it here on the chat as well. And then some of you can. You will sort yourself out. Ask each other. How do I get that? Please send it to Jim. Please send it to Jim. To who? To Jim. And then he's going to post it on our group. OK, I think he also has a copy. But I will ask him if he doesn't. Then I will share with him. All the two types. Who are the other two types that I have? How can I forget my colleagues? Those are my colleagues. Let's do this. Wait. Just want to stop the recording. The recording will also be available on. Thank you.