Let pxx x15 x 12345 zero elsewhere be the pmf of X Find PX

Let px(x) = x/15, x = 1,2,3,4,5, zero elsewhere, be the pmf of X. Find P(X = 1 or 2), P(1 / 2 LE X LE 5 / 2), and P(l LE X LE 2).

Probability of x=1,2,3,4,5 are given by:

P(x=1) = 1/15

P(x=2) = 2/15

P(x=3) = 3/15

P(x=4) = 4/15

P(x=5) = 5/15

a. P(X=1 or 2) = P(x=1) + P(x=2) = 1/15 + 2/15 = 3/15 = 1/5

b. P( 1/2 < x < 5/2) means probability that x is between 0.5 and 2.5, and as x can take only discrete values:

P( 1/2 < x < 5/2) = P(x=1) + P(x=2) = 1/15 + 2/15 = 3/15 = 1/5

P(1 <= x <= 2) = P(x=1) + P(x=2) = 1/15 + 2/15 = 3/15 = 1/5