0 Data TableTear RatingPlate Gap0.09 0.13 0.43 0.88 0.34 0.37 0.75 1.82 0.18 0.14 0.18 3.96 0.06 0.55 0.02 0.07 0.37 4.35 0.080.03 0.22 0.19 0.11 0.03 0.54 1.02 0.0...

Complete each table.
$$\begin{array}{|c|c|}\hline \text { Decimal } & \text { Its square } \\\hline 0.1 & \\\hline 0.2 & \\\hline 0.3 & \\
\hline 0.4 & \\\hline 0.5 & \\\hline 0.6 & \\\hline 0.7 & \\\hline 0.8 & \\\hline 0.9 & \\\hline\end{array}$$

All right. Let's just finish the table. So this is .1.0 5.025. 101 and Corn 005. Mhm. This other off our values. This one is given. So, we don't care of it. All right. So, let's fill up the rest of the table. The first thing say find zero. Fight right? And just right area .05 can convert it, which is the lap terrier. This .95. So, we find the table. We get this gallery is 1.64. It is 1.64. Yeah. All right. If we did the same thing to the outer mothers. So safe On 0-5, the right area is point nearly to fight left area Coin 97. White. Okay. The answer is 1.6. 1.96 The search warrant. We're actually covering the zero. Why? While the right terror is .01. That terror At the .99. Now we can get the dollar is two points for three. Last part. Now there are the apartment here is here, with life. Given the right areas on 005, the lab area is sexually porn 995 We can't get. The Bible is 2.58. Okay, If you're up this table, There was 1.96 here. There was 4.3 serie. It's a 2.58. This is our answer.

In question 18. It tells us to complete the expected value table when this table were given the exes and the probabilities of those exes and were asked to complete the third column, which would be x times its probability. So I'm gonna go through multiplies zero with zero point to get zero. One times 0.2 is your point to you. Two times 0.4 is your 0.8. Three times 0.2 is your 0.6?

This problem? Yes. Is too cube all of the numbers that are on the left side of the color and then put it in on the right side of the corn. So basically, what Cuban means is multiplying whatever is in its parentheses. Three times. So zero point one time, 0.1. What we discovered in the last problem is going to be 0.1 and then multiply that again. We're gonna get one zero zero, and now it's three decimal places compared to last time. So is your 0.2 terms. Your boy, too, is going to be 0.4 like we had discovered in the last problem. Let's play that this one is going to be just a little bit different. But either way, three dust won't places your 0.3 turns. Your 0.3 is your 0.9 times your 0.3. Know this to be 27 9 and three. Multiplying 93 together is 27 three decimal places. Final answer. All right, is your point for in your 0.0.4 is your 0.16 Let's play that again is where we're starting to get a little more complicated. Six times four is 24 carry over 64 three decibels. Final answer is your 0.5 times 0.5 is 25 times 0.5 five times five is 25. Carry over three desperate places. Notice that you're going to move it over three decimal places Every single times was your 0.6 times Your 0.6 is your 0.36 Time 0.6. It's gonna be 36 again eight times or excuse me. Six times three is 18 plus three is 21 three decibels. All right, seven times seven or it's near 0.7 10. 0.7 is your 0.49 times your 0.7. This is gonna be 63. Carry over the 6 28 four 123123 Same thing for 0.8. We know that. Is it? Your 0.8 squared is your 0.64 Multiply that again. What is your point? Eight. This is gonna be 32. Eight times six is 48 plus three is 51 three decimal places. Final answer and last one. You know that nine times nine is 81 at over the decimals. One more time to finalize for this one is your point 7 to 9

In this problem, we will be using what it means to be a probability distribution for a discrete random variable. To figure out whether the table to see on your screen are valid probability distributions. Or it's able to be a valid probability distribution. It must list all possible values with their corresponding probability. The probabilities must be between zero and one. And the some of the probabilities listed must equal one. Let's look at this first table. Um and it seems to be a table that lists possible values in the first row and the corresponding probabilities in the second row. Uh We can check if the probabilities are between zero and one, but we see here that one of the probabilities is negative, which means it's less than zero, so it's not between zero and one. And because it fails that second criterion, this cable is not a valid probability distribution because uh one of the probabilities, specifically the probability of random variable being zero is less than zero. Therefore failing the second criterion. Now, we can look at the second table and we can see that it seems to be a table again lists possible values in the first row with the corresponding probabilities in the second row. Um We can very quickly see that the probabilities listed are all between zero and one. And so the last thing to check is if the probabilities sum to one, I'm going to be using this big greek letter sigma to mean some of the P of X is. So that means we're just adding up all of the P of X. Is that would be the probability of one plus the probability of the random variable evaluating +22 plus the probability of the random variable evaluating +23 And we know those values it's given to us by the table. So a 0.46 plus 0.164 And when we add those all up we get 0.895 which is not equal. And so it fails that last criterion which says that the some of the probabilities must equal one. Therefore this is not a valid probability distribution again, because the probabilities do not so much one. Probabilities do not some 21 great. Now on to the final table, we can see again that it's a table that lists possible values with their force planning probabilities in the 1st and 2nd respectively. We can very quickly check that all of the probabilities listed are between zero and one. And so the last thing to check is if the some of the probabilities is equal to one. So the probabilities are all listed in this second rail right here. So I'm just going to copy those over adding them up. So 0.13 0.27 plus is 0.28 plus 0.18 plus 0.14 And we can uh add those all up and we actually do get one. Therefore it is a valid probability distribution, it's a valid probability distribution. Um because the uh well the probabilities are between zero and one, and the some of the probabilities is equal to one, which means that fits all of the criteria that we've seen that list above. And now we're done with the problem. Thanks for watching.