Question

A fair coin tossed 400 times.If X is the number of heads obtained, find the expected value and variance of X

Answer 1

We have a Binomial distribution,

$n=400,p=0.5,q=1-p=1-0.5=0.5.$

For a Binomial distribution the expected number of successes (a head obtained) and the variance are given by the formulas:

$\mu=np=400\cdot0.5=200,\\ \sigma^2=npq=400\cdot0.5\cdot0.5=100.$