1. The continuous random variable X is distributed with probability density function () = (4 ), 0 4 Find:

(i) the value of k

(ii) the probability, to three decimal places, that X will exceed 3.

2. A continuous random variable X has probability density function f, where () = 5 8 (4 4 ), 1 < < 1

(I) Check that this f is a valid probability density function.

(II) Calculate ( > 1 2 )

(III) Calculate ()and ()