The distribution of a random variable $X$ is given below \begin{array}{lllll} \hlineX=x & 1 & 2 & 3 & 4 \\ \hlineP(X=x) & 20 & 40 & 60 & 80 \\ \hline \end{array} Then, the standard deviation of $X$ is

• A

  4
• B

  $\frac{3}{2}$
• C

  2
• Correct answer
  D

  1

Solution

\begin{array}{ccccc} \hlinex & 1 & 2 & 3 & 4 \\ \hlineP_x=x & 2 c & 4 c & 6 c & 8 c \\ \hline \end{array} So, standard deviation of $X$ is Now, $2 c+4 c+6 c+8 c=1 \Rightarrow c=\frac{1}{20}$ for standard deviation
$$ \begin{aligned} & \sigma=\sqrt{\Sigma x^2 \cdot P x-(\Sigma x \cdot P x)^2} \\ & \Rightarrow \quad \sigma=\sqrt{10-(3)^2} \Rightarrow 1 \\ & \end{aligned} $$

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