Question

A lottery will be conducted for the benefit of the poor but deserving students ata certain school. Four hundred tickets will be sold. One ticket will win P2000and the other tickets will win nothing. If you buy one ticket, what will be yourexpected value and variance of your gain.​

Answer 1

If You buy one ticket the expected gain is x.

There are two possibilities:

lose → x=0 (nothing gain)

win → x = 2000 gain

The expected value μ is the sum of the product of each possibility x with its probability P(x):

$E(x) = μ = \sum xP(X) \\ = 0 + \frac{2000}{400} \\ = 5$

The expected value is 5.

The variance is the expected value of the squared deviation from the mean:

$σ^2 = \sum (x- μ)^2P(x) \\ = (0-5)^2 \times \frac{399}{400} + (2000-5)^2 \times \frac{1}{400} \\ = 24.93+4.98 \\ = 29.91$

The variance is 29.91.