Question

The officers of the Mathematics Club are planning to sell 280 tickets to be raffled during

the school’s foundation day. One ticket will win ₱5,000, two tickets will win ₱3,000, three

tickets will win ₱2,000 and the other tickets will win nothing. If you will buy one ticket,

what will be your expected value and variance of his gain?

Answer 1

Let X be the value of the gain. Then

$P\left( X=5000 \right) =\frac{1}{280}\\P\left( X=3000 \right) =\frac{2}{280}\\P\left( X=2000 \right) =\frac{3}{280}\\EX=5000\cdot \frac{1}{280}+3000\cdot \frac{2}{280}+2000\cdot \frac{3}{280}=60.7143\\EX^2=5000^2\cdot \frac{1}{280}+3000^2\cdot \frac{2}{280}+2000^2\cdot \frac{3}{280}=196429\\DX=EX^2-\left( EX \right) ^2=196429-60.7143^2=192742\\$