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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 8 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 8 Maths Textbook Solution.

Answers (1)

Answer:

-0.2.1.249

Hint:

MeanE\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} & -3 & -1 & 0 & 1 & 3 \\ \hline p_{i} & 0.05 & 0.45 & 0.20 & 0.25 & 0.05 \\ \hline \end{array}

Solution:

\begin{aligned} &\text { Mean } E(X)=\sum_{i=1}^{n} x_{i} p_{i} \\ &=(-3) \times 0.05+(-1) \times 0.45+0 \times 0.20+1 \times 0.25+3 \times 0.05 \\ &=-0.15-0.45+0+0.25+0.15 \\ &=-0.2 \\ &E\left(X^{2}\right)=\sum_{i=1}^{n} x_{i}^{2} p_{i} \\ &=(-3)^{2} \times 0.05+(-1)^{2} \times 0.45+0^{2} \times 0.20+1^{2} \times 0.25+3^{2} \times 0.05 \\ &=0.45+0.45+0+0.25+0.45 \\ &=1.6 \\ &\operatorname{Var}(X)=E\left(X^{2}\right)-(E(X))^{2} \end{aligned}

=1.6-(-0.2)

=1.6-(0.04)

=1.56

Standard deviation \sqrt{var}=\sqrt{1.56}=1.249

 

 

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