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  • Please Solve R.D.Sharma class 12 Chapter 31 Mean and Variance of a random Variable Exercise 31.2 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 2 Maths Textbook Solution.

Answers (1)

Answer:

\frac{1}{3}.\frac{23}{18}

Hint:

\sum_{i-1}^{n}p_{i}=1

Given:

\begin{array}{|c|c|c|c|c|} \hline X & 0.5 & 1 & 1.5 & 2 \\ \hline P(X) & k & k^{2} & 2 k^{2} & k \\ \hline \end{array}

Solution:

(i)

\begin{aligned} &\sum_{i=1}^{n} P\left(X_{i}\right)=1 \\ &k+k^{2}+2 k^{2}+k=1 \\ &3 k^{2}+2 k-1=0 \\ &3 k^{2}+3 k-k-1=0 \\ &(3 k-1)(k+1)=0 \\ &k=\frac{1}{3},-1 \\ &k \geq 0, k \neq-1 \\ &k=\frac{1}{3} \\ \end{aligned}

\begin{aligned} &\text { (ii) } E(X)=\sum_{i=1}^{n} X_{i} P_{i} \\ &=0.5 \times k+1 \times k^{2}+1.5 \times 2 k^{2}+2 k \\ &=4 k^{2}+2.5 k \\ &k=\frac{1}{3} \\ &=4 \times\left(\frac{1}{3}\right)^{2}+2.5 \times \frac{1}{3}=\frac{23}{18} \end{aligned}

 

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