Chapter 11.2, Problem 1MP

Let

$f\left(x\right)=\{\begin{array}{cc}6x-6x^2& \text{if}0\le x\le 1\\ 0& \text{otherwise}\end{array}$

Graph f and verify that f satisfies the first two conditions for a probability density function. Then find each of the following probabilities and illustrate graphically:

(A)     $P\left(.3\le X\le .8\right)$

(B)     $P\left(X\le .7\right)$

(C)     $P\left(X\ge .4\right)$

(D)     $P\left(X=.5\right)$