X and Y are discrete random variables with a joint density function as follow f(x, y) = 1) = {²+ ( x² + y) 0, (x² + y) x = 0,1,2; y = 0,1,2 Otherwise 1) Find the value of Cov[X, Y] 2) Find the value for both E(Y|X = 1) and E(X|Y = 2)

The random vector (X,Y) has the following joint probability density function:f(X,Y)(x,y) ={4xye−(x^2+y^2), x >0, y >0, 0, otherwise LetZ=√(X2+Y2) Find the probability density of the random variableZ.

3. An electronic system has one each of two different types of components in joint operation. Let Y, and Y, denote the random lengths of life of the components of type I and type II, respectively. The joint density function is given by 1 fV1, Y2) = 0, ,Y1 > 0, y2 > 0 elsewhere a) Find P(Y, > 1, Y2 > 1) b) Are Y, and Y, independent? c) What is the marginal distribution of Y,

4. Let X and Y be independent, continuous random variables with densities and fx(x) = = fy (y) = = 0 {} if 0 < x < 2 otherwise. y if 0