Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

In 5 tosses of a fair coin, let X be the number of heads minus the number of tails. For the probability distribution of X, what is the mean and variance?

share|improve this question
one way to get 5 heads and no tails and one way to get 5 tails and no heads. 5 ways to get 4 heads and 1 tail and 5 ways to get 4 Tails and 1 head. 10 ways to get 3 heads and 2 tails and 10 ways to get 3 tails and one head... does that help give you your distribution? –  Iceman Nov 30 '13 at 4:15

1 Answer 1

up vote 2 down vote accepted

$P(H-T=5)=\frac1{32}$ and $P(H-T=-5)=\frac1{32}$

$P(H-T=3)=\frac5{32}$ and $P(H-T=-3)=\frac5{32}$

$P(H-T=1)=\frac{10}{32}$ and $P(H-T=-1)=\frac{10}{32}$

So the mean $\mu$ would be


and the variance $\sigma^2$ would be


share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.