Chapter 6.6, Problem 65E

a.

To determine

Derive the joint density function for $U_1$ and $U_2$.

b.

To determine

Find the value of $E\left(U_1\right)$.

Find the value of $E\left(U_2\right)$.

Find the value of $V\left(U_1\right)$.

Find the value of $V\left(U_2\right)$.

Find the value of $Cov\left(U_1,U_2\right)$.

c.

To determine

Observe whether the random variables $U_1$ and $U_2$ are independent or not.

d.

To determine

Show that the random variables $U_1$ and $U_2$ have a bivariate normal distribution.

Identify the parameters of the appropriate bivariate normal distribution.