Answer to Question #315720 in Statistics and Probability for jeon

Question

Seven hundred tickets will be sold and these will be raffled during the fiesta of Brgy. Masiete. One of these tickets will win ₱10,000 and the rest will win nothing. What will be the expected value and variance of your gain if you will buy one of the tickets? 

Answer 1

Probability of win ticket is 1/700, not to win 699/700.

$XP(x)_{win}=10000\times1/700=14.3$

$XP(x)_{not win}=0\times699/700=0$

$\mu=\sum xP(x)=14.3+0=14.3$

$\sigma^2=\sum(x-\mu)^2P(x)=(0-14.3)^2 \frac{699}{700}+(10000-14.3)^2\frac{1}{700}=204.2+142448.9=142653.1$