Q.Find the mean and variance of the number of heads in 3 tosses of a fair coin.

Each toss is a Bernoulli trial with success probability $p=\dfrac{1}{2}$ (a head) over $n=3$ independent tosses, so $X\sim B(3,\,1/2)$ — apply mean $=np$ and variance $=npq$.

$n=3,\ p=\dfrac{1}{2},\ q=1-p=\dfrac{1}{2}$

Mean $=np=3\times\dfrac{1}{2}=\dfrac{3}{2}$ …