Question

The following distributional facts apply in this part: All variables are jointly normal and the marginals are as follows:

N(m,s ): This is the notation for the Normal distribution with mean m and standard deviations .

X~N(5,2) Y~N(2,3) Z~N(0,1) W~N(-4,6) U~N(0,5) V~N(24,1) Covariances between these variables are:
sxy =.4, sxw =-.5, swu =1, suv =2; allothercovariancesare0.

We have a random sample of size 6 from the distribution of X. We have a random sample of size 10 from the distribution of Y.

We have a random sample of size 12 from the distribution of Z. We have a random sample of size 4 from the distribution of W. We have a random sample of size 2 from the distribution of U. We have a random sample of size 8 from the distribution of V.

The sample means and variances of each of these samples is denoted in the usual way by X and S 2 with appropriate subscripts. In problems 5-8, find the distribution of the indicated random variables, and report the mean and standard deviation for Normal distribution. Report the degree(s) of freedom for t, Chi-square, and F distributions. If the random variable has no known distribution, write 'None.'

5. Find P[U > 2.1768Su ]

6. Find the value of d such that P[ (3(Y -2)2) /   ((W +4)2 ) < d ] =.95

Note: Y is not an order statistic; it is simply the first value in the sample from the distribution of Y.

7. Find Cov(2X - 5, Y + Z)

8. Find the variance of 3U-2W.

PLEASE DO ALL PARTS THANK YOU

Answer 1