Question

Let X have a uniform distribution on the interval (3, 13). Find the probability that the sum of 2 independent observations of X is greater than 24.

Answer 1

Solution:

Given that X have a uniform distribution on the interval (3, 13) i.e. X ~ [ 3,4,5,6,7,8,9, 10, 11, 12, 13]

We need to find the probability that the sum of any two independent observations is greater than 24.

There are total 11 numbers. So 1st and 2nd numbers can be selected in ways each.

Therefore, total combinations= 11×11=121

The total combinations whose sum is greater than 24 are-

(12, 13), (13,12) & (13,13)

i.e. only 3 possible combinations.

So,

Required probability= 3/121