A lottery game pays $500 with .001 probability and $0 otherwise.The variance of the payout is
A) 15.8.
B) 249.50.
C) 249.75.
D) 499.

Question

Quizplus · Accepted Answer

The variance of a discrete probability distribution can be found using the formula:
Var(X) = Σ [ (xi - μ)^2 * P(xi) ]
where xi is the payout for each possible outcome, μ is the expected payout, and P(xi) is the probability of each outcome.

In this case, we have two possible outcomes:
- $500 with probability 0.001
- $0 with probability 0.999

So we can calculate the expected payout as:
E(X) = $500 * 0.001 + $0 * 0.999 = $0.50

Using the formula for variance, we get:
Var(X) = (500 - 0.5)^2 * 0.001 + (0 - 0.5)^2 * 0.999
Var(X) = 249.75

Therefore, the best choice is C.

A Lottery Game Pays $500 with