00:01
Hi, i'm david and i'm here to help you answer your question.
00:03
In this question here we're given the joint distribution of the two random variables x and y now let me begin up here from the table here we need to answer the question one -by -one and here in the question a want to find the probability that the y smaller than 2 so why smaller than 2 it will be either the 0 or 1 and 2 and 2 make this some easier i'll bring this down and i will compute the total first.
00:39
So if we compute the total will be the probability of y that y equal to small y.
00:47
So we need to end up this one.
00:49
So when we end up we will have 0 .05 plus 0 .21 plus 0 .08 then we get equal to the 0 .38, sorry this one 34.
01:02
This one, if we end up, we have the 0 .01 plus 0 .0 .0.
01:06
1 plus 0 .15 equal to the 0 .36 and this one will have equal to the 0 .3.
01:19
Also this one will be the proper predictor x equal to the small x and it will add up this one has 0 .05 plus 0 .1 plus 0 .03 equal to 0 .18.
01:31
Here we have the 0 .21 plus 0 .11 plus 0 .19 equal to the 0 .01.
01:38
0 .51 0 .08 plus 0 .15 plus 0 .0 .08 equal to the 0 .31.
01:48
And now we are ready to answer the question 8.
01:51
Probably the why is smaller than 2.
01:54
It means that why can equal to the zone 1 only.
01:58
1 equals to the 0 .34.
02:01
1 equals to the 0 .36.
02:03
Then get equal to the 0 .70.
02:07
And then, when you find the probability of the y smaller than 2, and the x greater than 0.
02:15
It means that we will have to add up the dose quantity here only.
02:22
And then we will have this one equal to the 0 .21 plus 0 .11, plus 0 .08, plus 0 .15.
02:30
Then we get equal to the z -form 55 and for the question b i need to find the marginal density function of the x and y so it's already done here this will be the marginal density of the y and this will be the marginal density of the x and that will be done for the question b and then for the question out let me write it out explicitly for you for the question b we will have for the probability in the x x x can tell the value 0 1 and 2 for the 0 will be the 0 118 for the 1 will be the 0151 for the 2 will be the 0151 similarly for the y we have the probability in the y why why can turn the value 0 1 and 2 as well 014 736 7 3 for the question c we have to find the mean and funny some the x so e we have to find the mean and funny some the x so e the x equal to the summation in the x times the probability in the x we multiply them like a pair and then we add them up then have 1 times 0 .18 plus 1 times 0151 plus 2 times 0 .31 and then we get 0 .1 plus 0 .0 .3 plus 0 .3.
04:01
Sorry this one will be the 0 here so we have 0 .51 plus 2 times 0 .31 equal to the 1 .13 equal to the 1 .13 and we have the variance of the x that equal to the summation of the x minus the mean of the x square and then times when the probability of the x then we have the 0 minus the mean square time with the 018 plus 1 minus the mean square times 0151 plus the 2 minus the mean square times 0131 and if you compute it we have 0 minus the mean square 10 .18 plus 1 minus the mean square times 0 .151 plus the 2 minus the mean square times 0 .31 then it gets equal to the 0 .47 31 that will be the answer for the question c.
05:09
For the question d where to find the conditional probability that's the function of the 1.
05:19
Given the x equal to 1 and probability under y given the x equal to 1 and y equal to the 0 1 and 2 as well so given the x equal to the 1 so we just highlight the x equal to the 1 so we will take that probability here we will divide by the total so we have 0 .21 dividing by the 0 .501 then we get equal to the 0 .411.
05:53
I will round to the four decimal prices.
05:56
The next one will born 11 divided by the japan 51 and equal to the zabon 27 and the last one will be the 0 .19 divided by the 0 .51 equal to the 0 .37 25 and then we need to find the mean and variance as well.
06:19
So the mean of on the y given the x equal to 1 so we just equal to you we multiply them and then we add them up so we have 0 times with the 0 .1 118 plus 1 times what here we get the 1 time with the 0 .257 plus the 2 times with the 0 .37 255 and if you compute we have this one will be 10 to 157...