Chapter 4.2, Problem 11E

Suppose that Y possesses the density function

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

1. a Find the value of c that makes f(y) a probability density function.
2. b Find F(y).
3. c Graph f(y) and F(y).
4. d Use F(y) to find P(1 ≤ Y ≤ 2).
5. e Use f(y) and geometry to find P(l ≤ Y ≤ 2).