(a) The continuous random variable X has density function f(x) as defined below,
f(x) = {3/x^4, x > 1,
0, elsewhere.
(i) Verify that this is a valid density function.
(ii) EvaluateF(x).
(iii) Find P(X> 3).
(b) The continuous random variable X has density function f(x) as defined below.
f(x) = { (k(x + 2)², -2≤ x < 0
4k , 0≤x≤ 4/3
0, elsewhere.
(i) Find the value of the constant k.
(ii) Find the cumulative distribution function
(iii) Find P(-1≤x≤ 1).
(iv) Find. P(X> 1)
