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0,605I0 501lo 502I0 5020.50 5030399I0 504042 0.3 0 20 1ol}IDIplsx()063m...

Question

0,605I0 501lo 502I0 5020.50 5030399I0 504042 0.3 0 20 1ol}IDIplsx()063m

0,6 05 I0 501 lo 502 I0 502 0.5 0 503 0399 I0 504 04 2 0.3 0 2 0 1 ol} ID Ipls x() 063m



Answers

$$ \begin{array}{|c|cccc|}\hline x & {-5} & {-3} & {0} & {2} & {4} \\ \hline P(x) & {0.1} & {0.3} & {0.2} & {0.3} & {0.1} \\ \hline\end{array} $$

Low. Today we will be one skin continuing our discussion of probability distributions with an example of a distribution and will be determining if it is a probability is a a probability distribution or not. Now, to start with will be reviewing again. What a probability is region is. Definition is that it's a table or an equation that links each outcome of a statistical experiment with its probability of occurrence. And to determine if we're looking at probabilities is to be sure not. We have two rules number one all probabilities and the probability distribution must be between zero and one can have a negative can have anything greater than one cause then, well, they're not probabilities anymore. And number two, the sum of all over probabilities must equal one. Sorry, guys, only fix that. There we go. Now are probability that our distribution that we will be looking at today is it swallows. You have our X over our probability of X and our exes for today are three, 69 and one. Yeah, Eleanor probabilities are 0.3 0.40 point 30.1. The first things first we see that rule number one is being followed. We don't have any negative probabilities. And we don't have any probabilities greater than one. Now, for number two, Rule number two, we need our total to be equal. The one and we're gonna need to calculate that out. Now we have 0.3 plus point for 0.7. Wait three plus 30.1 to your 0.4. So, unfortunately, our total today it's 1.1 which does not equal one.

Okay. We got a lot of matrix multiplication here. Now, only two major modification. We do the rows of the first Matrix by the columns of the 2nd 1 We've got three by three matrix by three. Right three matrix. So well, number three by three matrix. So we've got first row against First column to lots of North 30.4 is no 0.8 plus knocking to one. They have a big one we can feel. What about majors? In their first for a second column? We have no point for minus and not pay for one and 10.2 years, which believe this is zero and finally first wrote that column. No point for lots here. And nobody to lots to know before on minus no point for nobody for might not wait for Sierra. Okay. Moving on to our second row first column, nor put two lots of 2.4 and then won a lot of money helping force gives to the zero second row. Second column. We're going one of our first out of one of our last moments. We have no way to piss. No 10.81 and second row, third column minus no point for two months. Not putting a one lot. Nominate. There's a council giving us a zero. OK, now we're finally going to buy last row. First column. We got to loss of minus nought. Point to which has no minus, no 00.0.4 on were out on a point for that zero, uh, third row, second column, minus no 0.2 plus no 0.20 And finally, third row, third column, nor 0.8 point four. And then we're gonna put two, which was one that this is actually identity matrix, so you'll find that these two major cities are in verse.

All right. Today we will be continuing our discussion of probability distributions. And before we look at the distribution for today to determine if it is a probability distribution or not, we're going to review the definition of probable distribution. And that is a table or an equation that links each outcome of a statistical experiment with its probability recurrence. We have to remember our two rules that go with probability distributions. Number one is that all probabilities in the probability distribution distribution must be between zero and one, and our second rule is that some of all probabilities must equal one. Now let's take a look at the crowd build. Sorry, let's take a look at the distribution we have today and see if we can determine if it is or is not a probability distribution. So today is our vents over probabilities. No, our events are five, seven and nine. The problem is there 0.6 zero point A and negative 0.4. Just from writing this out, we automatically see why this distribution can't possibly be a probability distribution. That's because we have our negative 0.4 probability right here, because that's not possible. It's not possible to have a negative probability, but let's ignore Rule number one for a second and just I just calculate the total probabilities are total of our probabilities. Anyway, we have our six and our eggs, so we have 1.4 here and we have a negative for sore total ends up Equalling one. So while rule to is followed, we can check that rule to is being followed. Fortune or a one rule one still isn't being followed, so we have to say that's a just distribution. It's not a probability distribution that's not possible.

Okay. I've got a matrix multiplication here on, uh, only dimension modification. We do the rose off the first matrix by the columns off the second matrix. So, for example, if I wanted to find the first row first column, I'd have to do first rate against the first column. So let's do that now. So what I have to lots of nor put four, which has no 40.8 plus one, love. No point to which gets takes us to one on an zero. Lots of the ever. So we just left with our want. Okay, let's go from our first road to 1st 2nd calm. NASA would be this entry here. Factory second collar, too. Let's not went to is no 0.4 minus one. A lot off, no point for, which is zero. So zero here, taking them out first. Right? But maybe not to ask that column to lots of miners. No 0.4 plus one. A lot of no 10.8. That's what's going on. If it is a rare Okay, moving down to our second run out first column, we have one laor each of these against two lots off each of these. You can see in the middle row. So let's go through this. Got no, but for minus two, lots of no point to which is gonna be a zero. Then we've got hit, nor 0.2 plus two does not point for which you give us a one and finally minus no point for plus two Lots of not put two, which is my stopping for plus not point for Give us zero. Okay, Federal first quote Here's got one law. This on one of this. No point to plus minus no points. A zero here. No put for minors, no point for zero. Who's got one of each member? And then here We've got a no 10.8 and your point to which was coming one on This is their identity matrix, so you'll find that these two major cities are actually inverse


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