2) Consider random variable X with the following probability density function: f(x) = 2x if 0 < x < 1, zero otherwise.
Let Y = 5X + 1.
a) Use the distribution function method to find the cumulative distribution function (cdf) of Y and then also the probability density function (pdf) of Y.
b) Use the transformation (change of variables) method to find the pdf of Y using the pdf of X.
3) Let X be an exponential random variable with cumulative distribution function (cdf):
F(x) = 1 - exp(-λx), x > 0.
If a simulated value of a Uniform (0, 1) random variable is given as U = 0.92015, find a simulated value of the random variable X.