The cumulative distribution function F_X(x) of a random variable X (which takes integer values only) is given by:

F_X(x) = 0 for x < 1

F_X(x) = 0.3 for 1 x < 2

F_X(x) = 0.45 for 2 x < 3

F_X(x) = 1.0 for x 3

1. Find the probability mass function P_X(x).
2. Find P(1 < X < 3)
3. Find P(3 < X < 5)