Answer to Question #310208 in Statistics and Probability for dino

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

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