Let X be a random variable that follows the Beta distribution with parameters a > 1 and B 1. The pdf of X is r(a+3) r(a)r(3)' f(x) = a-1(1 – a)-1, for 0

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A random variable X has range (0, 2), and p.d.f. given by Kx³ (1 - 12/7) 0 < x < 2, f(x)= Kr³ (1 where K is a suitable normalising constant. (a) Show that in order for f(x) to be a valid p.d.f. over the range (0, 2), the normalising constant K must be equal to 2. (b) Calculate the expected value of the random variable X.

The continuous random variable X on [-1,1] has pdf given by fx(x) = k(3x + 5) for x = [1,1] where k is a constant that you are going to determine. fx(x) = 0 outside the interval [-1,1] Hint: consider Calculate the following: i. k ii. E(X) iii. Var(X)