A continuous random variable X has distribution function

(i) Obtain an expression for the probability P(a

b) for a 0.
(ii) Verify that the density function of X is given by

iii) Calculate the expected value and the variance of X.
(iv) Find the distribution function, the mean, and the variance of the random variable Y = ????X, where ???? > 0 is a given constant.

F(t)= t