Consider the random process X(t) = Acos (@,t +0), where A and w, are real constants and 0 is a random variable uniformly distributed on the interval (0, t/2). Find the average power of X(t).

The joint PDF of two random variables X,Y is given byfXY(x, y) = {k e^(-y-x/4) , x > 0, y > 0                    0,                  otherwisea)  What is the value of k ?b)  Find the probability P( X<Y ).c)  Find P( 0<X<2 ).

A variable X has a probability function f(x, 0) = 0e 0x; x≥0 y >0. The parameter 0 is estimated using two different estimators of simple random samples of size two: 01 2x+4x2 and 2=4x+5x2 3 3 Select the best estimator for \theta by comparing the Mean Squared Errors

Suppose Y is a continuous random variable drawn from the uniform distributionon the interval [3, 4], that is, Y ∼ Uniform([3, 4]). Conditioned on Y = y, a second randomvariable X is drawn from the uniform distribution on the interval [0, y]. What is fX(x), thepdf of X?

Let X and Y have joint PDFfX,Y (x, y) = 3x^2y + 3xy^2 if 0 < x < 1, and 0 < y < 1                    0 otherwise.a)  Find the covariance of X and Y .b)  Find Var(X).c)  Find the correlation of X and Y  (X and Y have the same variance.)