Find the value of a that makes the following function a prob

Find the value of a that makes the following function a probability function: p(x) = a/x+1 for x - 0, 1, 2, 3 (and 0 otherwise).

Solution

Here,

P(0) + P(1) + P(2) + P(3) = 1

Thus,

a[1/(0+1) + 1/(1+1) + 1/(2+1) + 1/(3+1)] = 1

a(25/12) = 1

Thus,

a = 12/25 = 0.48 [ANSWER]