Question

Find the mean of number randomly selected from 1 to 15.

Answer 1

The sample space of the experiment is S = {1, 2, 3, …, 15}.

Let X denotes the number selected.

Then X is a random variable that can take values 1, 2, 3, …, 15.

Each number selected is equiprobable therefore

P(1) = P(2) = P(3) = … = P(15) = `1/15`

μ = E(X) = `sum_(i = 1)^n x_ip_i`

= `1 xx 1/15 + 2 xx 1/15 + 3 xx 1/15 + ... + 15 xx 1/15`

= `(1 + 2 + 3 + ... + 15) xx 1/15`

= `((15 xx 16)/2) xx 1/15`

= 8