Example 1

Suppose that a continuous random variable, X, has the probability density function (PDF) given below: \[ f_X(x)=\left\{ \begin{array}{ll} \frac{3}{2}x, 0 \le x \le 1\\ \frac{1}{4}, 5 \le x \le 6\\ 0, otherwise \end{array} \right. \]

1. What is the probability that $X$ is equal to 4?
2. What is the probability that $X$ is more than 4?
3. Find $F_X(5.6)$
4. Knowing that $X$ is more than $0.8$, what is the probability that $X$ is less than 5.6?
5. What is the $85_{th}$ percentile of $X$?