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  • Explain solution for RD Sharma maths class 12 chapter 31 Mean and Variance of a Random Variable exercise multiple choice questions question 3 maths textbook solution

Explain solution for RD Sharma maths class 12 chapter 31 Mean and Variance of a Random Variable exercise multiple choice questions question 3 maths textbook solution

Answers (1)

Answer:

              0.4

Hint:

              To solve this we use mean formula

Given:

              P\left ( X=3 \right )=2P\left ( X=1 \right ) and P\left ( x=2 \right )=0.3  then  P\left ( X=0 \right )

Solution:

\begin{aligned} &\text { Mean }=\sum_{i=0}^{3} X_{i} P\left(X_{i}\right)\\ &1.3=X_{0} P(X=0)+X_{1} P(X=1)+X_{2} P(X=2)+X_{3} P(X=3)\\ &1.3=0 \times P(X=0)+1 P(X=1)+2 \times 0.3+3 \times 2 \boldsymbol{P}(\boldsymbol{X}=\mathbf{1})\\ &1.3=0.6+7 P(X=1)\\ &1.3-0.6=7 P(X=1)\\ &0.7=7 P(X=1)\\ &P(X=1)=0.1 \end{aligned}
 

\begin{aligned} As we know, \sum_{i=0}^{n} P\left(X_{i}\right)=1 \end{aligned}

\begin{aligned} &P(X=0)+P(X=1)+P(X=2)+P(X=3)=1 \\ &P(X=0)+0.1+0.3+0.2=1 \\ &P(X=0)=1-0.6 \\ &P(X=0)=0.4 \end{aligned}

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