Hi David

Variance = E(X^2) - [E(X)]^2. For a coin, E(X^2) = 0.5 and E(X) = 0.5, so its variance is 0.25. Since two coins are independent, their variance = 0.25 + 0.25 = 0.5. Finally, the Variance (5*X) = 5^2*Variance(X). In this case, variance = (25)*0.25 = 6.25

How is E(X^2) and E(x) both .5?

Hi frank,

Because the coin has only two outcomes, given the assumption:
heads = 0
tails = 1

E(x) = average [0,1] = 0.5
E(x^2) = average [0^2, 1^2] = average [0,1] = 0.5

David