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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 6 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 6 Maths Textbook Solution.

Answers (1)

Answer:

1.6,1.49

Hint:

Mean =E(X)=\sum_{i=1}^{n} p_{i} x_{i}and Standard Deviation =\sqrt{\operatorname{Var}(X)}

Given:

\begin{array}{|c|c|c|c|c|} \hline x_{i} & 0 & 1 & 3 & 5 \\ \hline p_{i} & 0.2 & 0.5 & 0.2 & 0.1 \\ \hline \end{array}

Solution:

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

=0 \times 0.2+1 \times 0.5+3 \times 0.2+5 \times 0.1

=0+0.5+0.6+0.5

=1.6

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

=0^{2} \times 0.2+1^{2} \times 0.5+3^{2} \times 0.2+5^{2} \times(0.1)

=0+0.5+1.8+2.5

=4.8

\begin{aligned} &\operatorname{Var}(X)=E\left(X^{2}\right)-(E(X))^{2} \\ &=4.8-2.6 \\ &=2.2 \end{aligned}

Standard deviation =\sqrt{\operatorname{Var}(X)}=\sqrt{2.2}=1.49

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