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.

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

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

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

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