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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 2 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 2 Maths Textbook Solution.

Answers (1)

Answer:3,1.7

Hint:

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

Given:

\begin{array}{|c|c|c|c|c|} \hline x_{i} & 1 & 3 & 4 & 5 \\ \hline p_{i} & 0.4 & 0.1 & 0.2 & 0.3 \\ \hline \end{array}

Solution:

Mean \begin{aligned} &=E(X)=\sum_{i=1}^{n} p_{i} x_{i} \\ \end{aligned}

\begin{aligned} &=0.4 \times 1+0.1 \times 3+0.2 \times 4+0.3 \times 5 \\ &=0.4+0.3+0.8+1.5 \\ &=3 \\ \end{aligned}

\begin{aligned} &E\left(X^{2}\right)=\sum_{i=1}^{n} x_{i}^{2} p_{i} \\ \end{aligned}

\begin{aligned} &=1^{2} \times 0.4+3^{2} \times 0.1+4^{2} \times 0.2+5^{2} \times 0.3 \\ &=0.4+0.9+3.2+7.5 \\ &=12 \\ \end{aligned}

\begin{aligned} &\operatorname{Var}(X)=E\left(X^{2}\right)-(E(X))^{2} \\ &=12-9 \\ &=3 \\ &\text { Standard deviation }=\sqrt{\operatorname{Var}(X)}=\sqrt{3}=1.7 \end{aligned}

 

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