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  • Please Solve R.D.Sharma class 12 Chapter 31 Mean and Variance of a random Variable Exercise Fill in the Blanks Question 2 Maths Textbook Solution.

Please Solve R.D.Sharma class 12 Chapter 31 Mean and Variance of a random Variable  Exercise Fill in the Blanks Question 2 Maths Textbook Solution.

Answers (1)

Answer: - E\left(X^{2}\right)-[E(X)]^{2} \text { or } \sum_{i=1}^{n}\left(P_{i}\left(X_{i}\right)^{2}\right)-\left[\sum_{i=1}^{n}\left(P_{i} X_{i}\right)\right]^{2}

Hint: - You must know the rules for finding variance of Random variables.

Given: -

\begin{array}{ll} X: & x_{1} x_{2}----x_{n} \\ P(X): & p_{1} \quad p_{2}----p_{n} \end{array}

Solution:

\begin{aligned} \text { Variance } &=\operatorname{Var}(X)=E\left(X^{2}\right)-[E(X)]^{2} \\\\ &=\sum_{i=1}^{n}\left(P_{i}\left(X_{i}\right)^{2}\right)-\left[\sum_{i=1}^{n}\left(P_{i} X_{i}\right)\right]^{2} \end{aligned}

Where E(x) represents mean value for random variable x.

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