The probability distribution of a random variable $X$ is given by \begin{array}{l|r|r|r|r|c} \hlineX=X & 0 & 1 & 2 & 3 & 4 \\ \hlineP(X=x) & 0.4 & 0.3 & 0.1 & 0.1 & 0.1 \\ \hline \end{array} The variance of $X$ is

• Correct answer
  A

  $1.76$
• B

  $2.45$
• C

  $3.2$
• D

  $4.8$

Solution

Given,
$\begin{aligned} \text { Mean } \bar{x} & =\sum_{i=0}^4 p_i x_i=1.2 \\ \text { Variance } & =\sum_{i=0}^4 p_i x_i^2-\bar{x}^2 \\ & =3.20-1.44=1.76\end{aligned}$

Hence, the correct answer is option: 'A'.