Chapter 4.3, Problem 21E

If, as in Exercise 4.17, Y has density function

$f\left(y\right)=\{\begin{array}{l}\left(3/2\right)y^2+y,\text{ 0}\le y\le 1,\\ 0,\text{elsewhere,}\end{array}$

find the mean and variance of Y.

4.17 The length of time required by students to complete a one-hour exam is a random variable with a density function given by

$f\left(y\right)=\{\begin{array}{l}c{y}^2+y,\text{ 0}\le y\le 1,\\ 0,\text{ elsewhere}\text{.}\end{array}$

1. a. Find c.
2. b. Find F(y).
3. c. Graph f(y) and F(y).
4. d. Use F(y) in part (b) to lind F(–1), F(0), and F(1).
5. e. Find the probability that a randomly selected student will finish in less than half an hour.
6. f. Given that a particular student needs at least 15 minutes to complete the exam, find the probability that she will require at least 30 minutes to finish.