Suppose that a random variable Y has a probability density function given by

f(y) = { 3/y^4 , if Y 1 and

0, if Y< 1}

(i) Determine the distribution function F(y) = P(Y y).

(ii) Calculate the 95th percentile of the distribution. Determine the value of 4 such that P(Y a) = 0.95.

(iii) Calculate the mean, E[Y], and variance, ;[V] of Y