Problem 4 (10 points):
Errors in an experimental transmission channel are found when the transmission is checked by a certifier that detects missing impulses. The number of errors found in an eight bit-byte is a random variable with the following distribution:
$$F(x) = \begin{cases} 0.0 & x < 1 \\ 0.6 & 1 \le x < 3 \\ 0.9 & 3 \le x < 7 \\ 1.0 & 7 \le x \end{cases}$$
(a) P(X <= 4), (b) P(X > 7), (c) P(X <= 3), (d) P(X > 3), (e) P(2 < X <= 4)