PROBABILITY QUESTION. Very tough.?

Question

your winnings can either be 15$, 10$, 5$, or 0$. Your odd's of attaining each are .25. The mean is 7.5, what is the standard deviation?

Answer 1

Variance = E(X^2) - [E(X)]^2

E(X^2) = sum of all X of X^2 * p(x)
E(X^2) = (.25)(225+100+25+0)
E(X^2) = 87.5

Variance = 87.5 - (7.5^2)
Var = 87.5 - 56.25 = 31.25

Std. deviation = square root of variance = 5.59