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Enr 04 Laraklztn Fjpobt0 213 hpslr Irxi, /6 1Ru4"6m034#[4716 enealn canranst> Icol ~uu[ Recnin0...

Question

Enr 04 Laraklztn Fjpobt0 213 hpslr Irxi, /6 1Ru4"6m034#[4716 enealn canranst> Icol ~uu[ Recnin0

Enr 04 Laraklztn Fjpobt0 213 hpslr Irxi, /6 1Ru4"6m034#[4716 enealn canranst> Icol ~uu[ Recnin 0



Answers

$$ \left[\begin{array}{lll|l} {1} & {0} & {4} & {4} \\ {0} & {1} & {3} & {2} \\ {0} & {0} & {0} & {0} \end{array}\right] $$

And this exercise, we're being given a table of data. The input is years from 1998, and two years increments. The output is the value of 3247: 5836. And we're being asked to find a model equation that would fit that data in quadratic form using translations, A H and K. Right? I have a graft all of that data here in Desmond's that we can look at it. I can see that it starts here at 1997. I'm sorry. at 1998 with the value of 3247 between 3000 and 3500 and the rate of increase gradually gets faster so that it looks like the values are getting higher more quickly. It's curving up, it looks like it might be a good candidate for a quadratic model. We could just start by using this initial point 1998 as the vertex of that. For Avalon I'm going to do that. That means that my starting year is shifting from 0 to 1998 to change that starting point and subtracting 1998 from the input and then To get the Vertex all the way up to 3247. I need to add that. That was my K value. If my stretch factor is just one, if it's a regular shape, I can see that. Yes, the problem goes through that. That's a fact vertex. It's very shallow right now because this scale is going in increments of 500. Every measure Interval, every major grid line represents 500. So it's being compressed a lot by the scale over the graph. My next task is to figure out what is the stretch factor A. That will make that problem fit the rest of data. So let's switch over to this whiteboard. I have already said that I am using the first point for my H and K values to get that vertex. So I'm going to rewrite my equation with this 0.0.1998 and 3247 ordered pair plugged in as my hk I'm shifting my starting year 1998. Yeah mm I am shifting my starting value up to 3247 247 So that's the beginning of my equation. Let me a great that seven. Better. I need to find this stretch factor. What I'm going to do is use another point of data. I've got this 0.0.2006 gives me 5,836 as an output. Yeah, That point has to be part of this equation. So if I put that X. Value 2006 in I need to get that 5,836 out. And that means I have to have an a value a stretch value that will make that work. So I'm going to do exactly that. I'm going to plug that point in with the input in the X. And the output in the UAE and then I'm going to solve to find out what a value makes that true so. Mhm. My y value is going to be 5836 if I have the right stretch factor. Mhm. When my input is 2006. Okay from this parable that's been shifted To a new starting year of 1998 and shifted up to give me a starting value Of 3247. Yeah. Mhm. Now I've got the equation I can solve for a, I'm going to start with parentheses. E. Is figure out what this is. So 5836 equals whatever my stretch value is, my stretch factor, 2006 19-1998 is eight years. That's still going to be squared plus 3,247. I can subtract 3247 from both sides and When I do that 5836 -3247 is 2589 equals a times eight squared eight squared to 64. So that gives me 64 Times my stretch factor. If I divide both sides by 64, 2589 Divided by 64 will give me my stretch factor. And when I put that into a calculator I get that that stretch factor a equals About 40.4. So value that I've calculated from this gives me 40.4. I'm going to go back to my graph And just check and see if that actually makes sense. Let's go back to Dez most if my a value is about 40, it fits This endpoint. If I put in 40.4 it does go through this end point but it's a little low. It doesn't include all of the other points which is never going to happen with real data. You're never going to get the curve that goes through all of the points exactly. But all of these points are above the curve which means that my model is a little love. I want to model that kind of includes all of the data. It doesn't have to go through all of the data so much as it goes through the middle of all of the data. So I'm going to try just a slightly larger value. 44. I've got one point that's too low and I've got three points that are above 45 is a little closer to the points that are above 46. Dance around 2048. It's kind of like 48 each. That's too big. Just testing to see what looks like balances the points the most. I think maybe like 48 is a good middle of the road. I've got three points that are a little above the curve. I've got one point that's quite a bit below the curve. So I would say a is anything between 44 and 48 is going to be a good model. I personally like 48. So I'm going to say about my model for this data. Yes. My health put value. Why Is equal to 48- nine years? My input year X- My starting year, 1998. Yeah. All squared plus. You make that squared better plus a shift up of 5,836. And that is my quadratic model for this data. Yeah.

In this problem, we have given the mattresses on be an oxidant remind video. The pair of each metrics is the inverse off each other. Let's consider it Mac tricks be find metrics. Be post refined, a productive metrics A and B begin the metrics which is equals toe identity mattress. Now they find a productive be into a The result of markets would be my 00 010 three do which is not equal ist white into Demetris Since the product of too many places on either side are not I'd into demand tricks. The given to my prisons are not in rows on each other.

In this video, we're gonna go through the answer to question number seven from chapter 9.5 West to find the argon values nine vectors off the matrix A given here. First. Do that. We need to find the determinant off the matrix. A minus. I ascetic with syrup. So this is the determinant. Off one minus R zero zero two three minus. Ah, one 0 to 4 months are You're wasting your over the top road Got one minus r times by the deterrent box Right to Buddy Matrix, which is remind us ah times by four minus R minus two. This is gonna be a one minus ah times by Ask what minus for our minus three hours. Minus seven are plus 12 minus to which is plus 10. Good. Then we can characterize this with one minus R and it's gonna factor Rise to be Ah. Minus five, uh, minus two. So we said that equal to zero. Then solve we're gonna have I can Values are is equal to one. I was equal to two on our secret five. There are three aiken values. Find their associates. I connect this starting first with I come back to rise. Because of what? When it's find the matrix a minus one times high times, the fact that you want is equal zero up. This is just 000 Good two to you. One on zero two three touched by yuan is equal to zero safe. Let's complete this by hand. So if you want, let's let the components be ex wives that then from the second World, we've got that to x close Thio. Why course Zed is equal to zero on from the third room we've got there, too. And two, Why close? Three is equal to zero. Okay, so this his bottom equation tells us that, uh, why is equal to minus three over two times that on the top equation tells us that thanks is equal to minus that minus half that minus why that's minus half said, plus three up to said. That's just ones that so, So X equals said, Let's just let them be ones. And that why's it was minus three or two time times said, which is just three. Everything. That's a first I Greta, the 2nd 1 we calculate with a minus, the less I connect it was too. Okay. Months to I times you want you could see. Right. That's gonna be a minus. 100 two 11 zero two four months. Two is two tells about you want zero? So the first hotels is not the first component. If you want equal to zero, then the bond to Rose. Tell us that Thea, the second and third components are next to each other. So if the 2nd 1 is one that the books reminds one, let's find the third Aiken Vector. Yeah, I can. Value was five comes I times you What do you want? It was there. So therefore months 400 two minus 21 02 minus one you want you see what Zephyr therefore you want? Well, the first component cto read off. That's just gonna be zero then. Second and for components are gonna be Will be, uh, yeah, we can tell from the second or the third World that if the second component is one, then the third component is twice second bone in, which is just too. That's a final act of Beckett

Today we will be continuing our discussion of probability distributions with an example of a distribution and determining if it is a probability distribution for not now. Before we determine if this is or is not a probability distribution, we first need to review the definition of probability distribution as well as the two rules that accompany it. No, start with probability. Distribution is a table or an equation that links each outcome of his statistical experiment with its probability of occurrence. And, of course, the two rules that a company that our number one the all probabilities in the probable distribution must be between zero and one. We cannot have negative probabilities, and we cannot have probabilities larger than one. We can't suddenly have a probability of two because that's just not possible. And her second rule is that the sum of all probabilities must equal one. You're determining the probabilities of the entire sample space essentially, So all the probabilities combined must equal one because you can't just have extra probabilities that don't contribute to the overall instances occurring. Now the distribution will be looking at today is her ex sir X over our probabilities of x three day. Oh, our exes are negative. Five negative three. There we go. 30 two and four. Sorry, we don't need those lines there. My mistake. Here we go. And our probabilities are 0.1 to your 0.3 0.2 0.30 point one. Now, first thing we see after writing it out, writing out her distribution, we see that number Rule number one has followed. All of our probabilities are between zero and one. We don't have any negatives. And we don't have anything greater than one. No. For rule number two, which is the sum of all our probabilities must equal zero total. This quit one plus 0.3 so well right down here. 0.4 went to 1.3 point five 0.1 0.5 plus 0.4 is not 0.9. Sorry. Plus 0.1. Our total does indeed equal ones. Based on that rule number two is also followed. So this distribution is probability distribution. All our rules were followed and it is table that links each outcome of whatever this statistical experiment ISS with its probabilities of occurrence


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