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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 5 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 5 Maths Textbook Solution.

Answers (1)

Answer:

2,1

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|} \hline x_{i} & 1 & 2 & 3 & 4 \\ \hline p_{i} & 0.4 & 0.3 & 0.2 & 0.1 \\ \hline \end{array}

Solution:

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

=1 \times 0.4+2 \times 0.3+3 \times 0.2+4 \times 0.1\\

=0.4+0.6+0.6+0.4\\

=2

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

=1^{2} \times 0.4+2^{2} \times 0.3+3^{2} \times 0.2+4^{2} \times 0.1\\

=0.4+1.2+1.8+1.6\\

=5

\begin{aligned} &\operatorname{Var}(X)=E\left(X^{2}\right)-(E(X))^{2} \\ &=5-4=1 \end{aligned}

Standard deviation =\sqrt{\operatorname{Var}(X)}=\sqrt{1}=1

 

 

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