2.33. Suppose that the random variables X and Y have a joint density function given by fx, y) = {c(2x + y) 2 2), (e) P(X >3), (f) P(X + Y >4), (g) the joint distribution func- tion, (h) whether X and Y are independent. (a) The total probability is given by

A: It is not multiplication.

A: giveny3=x4+3xdiffrentiate with respect to x3y2y'=4x3+3y'=4x3+33y2

A: To evaluate the following integral

A: We have to use the quotient rule , so we assume u and v and find u' and v'

A: To find:

A:

A: To calculate the length of the asteroid of

A: Given  x2y+x3+2y2=5y Apply power rule to take derivative We know that , derivative of x is 1  and…

A:

A:

A: We will start with the substitution, csc-1(2y) = x and apply the integration by parts. And, will use…

A:

A:

A: