Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

Please Solve R.D.Sharma class 12 Chapter 31 Mean and Variance of a random Variable Exercise 31.2 Question 1 Sub Question 4 Maths Textbook Solution.

Answers (1)

Answer:

$1,1.5$

Hint:

Mean $=E\left ( X \right )$ and Standard Deviation $=\sqrt{var\left ( X \right )}$

Given:

$$$ \begin{array}{|c|c|c|c|c|c|} \hline x_{i} & -1 & 0 & 1 & 2 & 3 \\ \hline p_{i} & 0.3 & 0.1 & 0.1 & 0.3 & 0.2 \\ \hline \end{array}$

Solution:

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

$=-1 \times 0.3+0 \times 0.1+1 \times 0.1+2 \times 0.3+3 \times 0.2$

$=-0.3+0.1+0.6+0.6$

$=1$

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

$=(-1)^{2} \times 0.3+0^{2} \times 0.1+1^{2} \times 0.1+2^{2} \times 0.3+3^{2} \times 0.2$

$=0.3+0.1+1.2+1.8$

$=3.4$

$\operatorname{Var}(X)=E\left(X^{2}\right)-(E(X))^{2}$

$\begin{aligned} &=3.4-(1)^{2} \\ &=2.4 \end{aligned}$

$Standard deviation =\sqrt{\operatorname{Var}(X)}=\sqrt{2.4}=1.5$

Posted by

infoexpert21

View full answer

Crack CUET with india's "Best Teachers"

HD Video Lectures
Unlimited Mock Tests
Faculty Support

cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Time Table 2027 LIVE: Class 10, 12 date sheet soon at cbse.gov.in; direct link, exam patterns, pass marks

anam-khan

CBSE Date Sheet 2027 Live: Class 10, 12 exam dates soon; LOC submission process, paper pattern

anam-khan

CBSE Exam Date 2027 Highlights: Class 10, 12 exam dates soon on cbse.gov.in; private candidate form

Latest Question