Mathematics Worksheet

Question 3Let X be a continuous random variable with PDF
and let Y = X².
a. Find the CDF of Y.
b. Find the PDF of Y.
c. Find E[Y].
5
fx (x) 32
{
=
0 < x < 2 otherwiseQuestion 4 Waiting time, X, at a certain restaurant has the following distribution. fx(x) = { Cr(1 0 Сx(1 − x) 0 < x < 1 otherwise a. Find the value of the constant C. b. Find the mean waiting time. c. Find the variance of waiting time. d. If the time spent by the customers in the restaurant is found to be a function of the waiting time as follows, Y = 5X – X² + 2, find the mean time spent by the customers in the restaurant.