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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 7 Maths Textbook Solution.

Please Solve R.D.Sharma class 12 Chapter 31 Mean and Variance of a random Variable  Exercise 31.2 Question 1 Sub Question 7 Maths Textbook Solution.

Answers (1)

Answer:

0,1.095

Hint:

Mean=E\left ( X \right )=\sum_{i-1}^{n}p_{i}x_{i}and Standard Deviation =\sqrt{var\left ( X \right )}

Given:

\begin{array}{|c|c|c|c|c|c|} \hline x_{i} & -2 & -1 & 0 & 1 & 2 \\ \hline p_{i} & 0.1 & 0.2 & 0.4 & 0.2 & 0.1 \\ \hline \end{array}

Solution:

\begin{aligned} &\text { Mean } E(X)=\sum_{i=1}^{n} x_{i} p_{i} \\ &=(-2) \times 0.1+(-1) \times 0.2+0 \times 0.4+1 \times 0.2+2 \times 0.1 \\ &=-0.2-0.2+0+0.2+0.2 \\ &=0 \\ &E\left(X^{2}\right)=\sum_{i=1}^{n} x_{i}^{2} p_{i} \end{aligned}

\begin{aligned} &=(-2)^{2} \times 0.1+(-1)^{2} \times 0.2+0^{2} \times 0.4+1^{2} \times 0.2+2^{2} \times 0.1 \\ &=0.4+0.2+0+0.2+0.4 \\ &=1.2 \\ &\operatorname{Var}(X)=E\left(X^{2}\right)-(E(X))^{2} \\ &=1.2-0 \\ &=1.2 \\ &\text { Standard deviation }=\sqrt{\operatorname{Var}(X)}=\sqrt{1.2}=1.095 \end{aligned}

 

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