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  • Please Solve R.D.Sharma class 12 Chapter 31 Mean and Variance of a random Variable Exercise Very Short Answer Type Question 3 Maths Textbook Solution.

Please Solve R.D.Sharma class 12 Chapter 31 Mean and Variance of a random Variable  Exercise Very Short Answer Type Question 3 Maths Textbook Solution.

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Answer: - 3.5

Hint: - You must know the rules of solving probability distribution problems.

Given: - If X denotes the number on the upper face of a cubical die when it is thrown, find the mean of X.

Solution: - A cubical die can show 1, 2, 3, 4, 5, and 6 on its face.

\begin{array}{|c|c|c|c|c|c|c|} \hline x_{i} & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline p_{i} & \frac{1}{6} & \frac{1}{6} & \frac{1}{6} & \frac{1}{6} & \frac{1}{6} & \frac{1}{6} \\ \hline x_{i} p_{i} & \frac{1}{6} & \frac{2}{6} & \frac{3}{6} & \frac{4}{6} & \frac{5}{6} & \frac{6}{6} \\ \hline \end{array}

\begin{aligned} &\text { Mean }=\sum_{i=1}^{6} p_{i} x_{i} \\\\ &=p_{1} x_{1}+p_{2} x_{2}+p_{3} x_{3}+p_{4} x_{4}+p_{5} x_{5}+p_{6} x_{6} \\\\ &=\frac{1}{6}+\frac{2}{6}+\frac{3}{6}+\frac{4}{6}+\frac{5}{6}+\frac{6}{6} \\ &=\frac{21}{6} \\\\ &=3.5 \end{aligned}

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