# Question: the random variable x has the probability density function given...

###### Question details

The random variable X has the probability density function given by:

f(x) = ax + b for 0 < x < 1

0 otherwise

where a and b are constants. Suppose that E(X) = 1/3.

i. Show that a = −2 and b = 2. (4 marks)

ii. Compute Var(X). (4 marks)