Let X denote the number of talls in two tosses of a coin. If the mean and the variance of X are $\mu $ and $σ^2$ respectively, than $\mu + σ^2 $ is equal to :

$\frac{3}{2}$

The correct answer is Option (1) → $\frac{3}{2}$

X → No. of tails (in 2 tosses)

$μ=E(X)=∑P_i(X)X_i=\frac{1}{2}+\frac{1}{2}=1$

$E(X^2)=∑P_i(X){X_i}^2=\frac{1}{2}+1=\frac{3}{2}$

$σ^2+μ=E(X^2)-E^2(X)+E(X)$

$=\frac{3}{2}-1+1$

$=\frac{3}{2}$