Math 483 Exam 1, Fall 2017 Name_________
6. If the distribution function of X is given by
$$F(x) = \begin{cases} 0, & x < 0; \\ \frac{1}{2}, & 0 \le x < 3; \\ \frac{2}{3}, & 3 \le x < 5; \\ \frac{11}{12}, & 5 \le x < 8; \\ 1, & x \ge 8. \end{cases}$$
a) calculate the probability mass function of X.
b) $$P(X < 4)$$