Question

Find the mean and variance of the 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 selected number.

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

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

E(X) = `sum_("i" = 1)^"n" x_"i""P"_"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

Var(X) = `(sum_("i" = 1)^"n"x_"i"^2"p"_"i") - (sum_("i" = 1)^"n"x_"i""p"_"i")^2`

= `1^2 xx 1/15 + 2^2 xx 1/15 + 3^2 xx 1/15 + ... + 15^2 xx 1/15 - (8)^2`

= `(1^2 + 2^2 + 3^2 + ... + 15^2) xx 1/15 - (8)^2`

= `((15 xx 16 xx 31)/6) xx 1/15 - (8)^2`

= 82.67 – 64

= 18.67