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Please Solve R.D.Sharma class 12 Chapter 31 Mean and Variance of a random Variable Exercise 31.2 Question 1 Sub Question 4 Maths Textbook Solution.

Answers (1)

Answer:

$1,1.5$

Hint:

Mean $=E\left ( X \right )$ and Standard Deviation $=\sqrt{var\left ( X \right )}$

Given:

$$$ \begin{array}{|c|c|c|c|c|c|} \hline x_{i} & -1 & 0 & 1 & 2 & 3 \\ \hline p_{i} & 0.3 & 0.1 & 0.1 & 0.3 & 0.2 \\ \hline \end{array}$

Solution:

Mean $=E(X)=\sum_{i=1}^{n} x_{i} p_{i}$

$=-1 \times 0.3+0 \times 0.1+1 \times 0.1+2 \times 0.3+3 \times 0.2$

$=-0.3+0.1+0.6+0.6$

$=1$

$E\left(X^{2}\right)=\sum_{i=1}^{n} x_{i}^{2} p_{i}$

$=(-1)^{2} \times 0.3+0^{2} \times 0.1+1^{2} \times 0.1+2^{2} \times 0.3+3^{2} \times 0.2$

$=0.3+0.1+1.2+1.8$

$=3.4$

$\operatorname{Var}(X)=E\left(X^{2}\right)-(E(X))^{2}$

$\begin{aligned} &=3.4-(1)^{2} \\ &=2.4 \end{aligned}$

$Standard deviation =\sqrt{\operatorname{Var}(X)}=\sqrt{2.4}=1.5$

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