1. Let X₁ and X₂ be two independent random variables with the probability density function of X, given by
F(x)= 1/xin2, x € (0.5, 1)
0, else. [6 marks] (a) Determine the probability density function of Y = X₁X₂.
(b) Determine the probability density function of
z= Y, Y € (0.5, 1)
2Y, Y € (0.25, 0.5]