Suppose the joint density function of X and Y is defined as, S(x,y) = 0sxS ys 2 Calculate the conditional expectation of X, given that Y = 1 а) 2 b) 2 c) 1.5 1 d)
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- Suppose you choose a real number X from the interval [2, 10] with a density function of the form f(x) = Cx, where C is a constant.(a) Find C.(b) Find P(E), where E = [a, b] is a subinterval of [2, 10].(c) Find P(X > 5), P(X < 7), and P(X2 − 12X + 35 > 0).Step 3: Expression for density function of T, in the convolution, isn't (t-s1) term extra?Please answer both parts of Question 1. Show all work. 1.) Suppose that Y1 and Y2 has a joint density function given by f(y1, y2) = c, 0 <= y1 <= y2 <= 1 0, elsewhere a) for U = Y1 + Y2, find the probability density function b) What is E[U]?