Edited By Lovekush kumar saini | Updated on Jan 25, 2022 04:38 PM IST

We all know that the Class 12 RD Sharma chapter 31 exercise 31.2 solution is one of the most outstanding solutions in the entire country for maths subjects for CBSE class 12 students. The RD Sharma class 12th exercise 31.2 can be considered an elite study material as any student will always recommend the solution and especially the ones who have passed the exams with great scores and have seen the fruitful result if practicing from this solution.

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Mean and Variance of a random Variable Exercise 31.2 Question 1(i)

Mean:

Standard deviation

Mean and Variance of a random Variable Exercise 31.2 Question 1(ii)

Mean

Mean

Mean and Variance of a random Variable Exercise 31.2 Question 1(iii)

Answer:Hint: Mean

Standard Deviation

Given:

Solution:

Mean and Variance of a random Variable Exercise 31.2 Question 1(iv)

Meanand Standard Deviation

Mean

Mean and Variance of a random Variable Exercise 31.2 Question 1(v)

Meanand Standard Deviation

Mean

Mean and Variance of a random Variable Exercise 31.2 Question 1(vi)

Meanand Standard Deviation

Mean

Mean and Variance of a random Variable Exercise 31.2 Question 1(vii)

Meanand Standard Deviation

Mean and Variance of a random Variable Exercise 31.2 Question 1(viii)

Meanand Standard Deviation

Standard deviation

Mean and Variance of a random Variable Exercise 31.2 Question 1(ix)

Answer:Hint:

Meanand Standard Deviation

Given:

Solution:

Mean

Mean and Variance of a random Exercise 31.2 Question 4

Three coins are tossed

Set ‘X’ be the random variable for tail

Mean and Variance of a random Exercise 31.2 Question 5

Mean , variance , standard deviation

Standard deviation

Number of kings in 52 cards

Let number of kings be X

P (X=0) = P (Number of kings)

Mean and Variance of a random Exercise 31.2 Question 6

Three coins are tossed

Let ‘X’ be the random variable for tail

Mean and Variance of a random Exercise 31.2 Question 8

Let X be the random variable which denotes the minimum of two numbers which appears

Mean and Variance of a Random Variable Exercise 31.2 Question 9

A fair coin tossed 4 times

Mean and Variance of a Random Variable Exercise 31.2 Question 10

A fair dice is tossed

Mean and Variance of a Random Variable Exercise 31.2 Question 11

A fair dice is tossed

Mean and Variance of a Random Variable Exercise 31.2 Question 12

Answer:Hint:

A fair coin tossed four times

X denotes the occurrence of head

Sample space

Mean and Variance of a Random Variable Exercise 31.2 Question 13

Mean = 2.3

Variance = 5

Hint:

There are 5 cards numbered 1, 1, 2, 2 and 3

There are 5 cards numbered 1, 1, 2, 2 and 3

Let, x = sum of two numbers on card =2, 3, 4, 5

Y = Maximum of two numbers = 1, 2, 3

Thus the probability distribution of x is given by

Total number of cards = 5 (2 cards with “1” + 2 cards with “2” + 1 card with “3”

Total number of possible choice (in drawing the two cards) = number of ways in which threw two cards can be drawn from the total 5

Probability that the two car drawn would be having the number 1 and 1 on them is P (11)

Probability that two cards drawn would be having the number 1 and 2 on them is P (11)

"1" and "2" on them

"1" and "3" on them

"2" and "2" on them

"2" and "3" on them

Probability for the sum of the members on the cards drawn to be

The probability distribution of x would be

Calculations for mean and standard deviation

The expected value of the sum

Expectation of x

Variance of the sum of the numbers on the cards

Standard deviation of the sum of the numbers on the cards

Computation of mean and variance

Thus the probability distribution of Y is given by

Computation of Mean and Variance

Mean and Variance of a Random Variable Exercise 31.2 Question 14

Variance

A die is tossed twice a “success” of getting odd number of toss

Mean and Variance of a Random Variable Exercise 31.2 Question 16

Person loss 10 rupees and get 90 rupees.

P (Wheels/Getting same slot)

Mean and Variance of a Random Variable Exercise 31.2 Question 17

Mean

Three cards are drawn at randomly from a shuffle pack of 52 cards

In 52 cards

26 = Red

26 = Black

Number of outcomes

3 Red 0 Black

2 Red 1 Black

1 Red 2 Black

0 Red 3 Black

Mean and Variance of a Random Variable Exercise 31.2 Question 18

Mean

An urn contains 5 red 2 black balls. Two balls are randomly drawn, without replacement.

Mean and Variance of a Random Variable Exercise 31.2 Question 19

Mean

Positive integer 2, 3,4,5,6 and 7

Mean and Variance of a Random Variable Exercise 31.2 Question 20

Mean

A die has thrown

Mean and Variance of a Random Variable Exercise 31.2 Question 21

Mean

A pair of dice are thrown

Mean and Variance of a Random Variable Exercise 31.2 Question 22

**Answer:**

(i) (ii) Mean (iii) Variance**Hint:****Given:****Solution:**

(i) We know that

(ii) Mean

The RD Sharma class 12 solution of Mean and Variance of a Random Variable exercise 31.2 comprises of two-level questions which varies from easy to moderate to tough, which consists of a total of 33 questions covering the essential concepts of the chapter mentioned below-

Probability distribution

Mean of a discrete random variable

Standard deviation

Mean of any probability distribution

Well, the RD Sharma class 12th exercise 31.2 is recommended by experts for several reasons mentioned below:-

The RD Sharma class 12 solutions chapter 31 exercise 31.2 can be downloaded from the Careers360 website for free of cost.

The RD Sharma class 12th exercise 31.2 consists of questions that have the chances that they might be asked in the board exams as observed previously.

The RD Sharma class 12 chapter 31 exercise 31.2 can also be used by teachers for preparing lectures and also question papers for school exams.

The RD Sharma class 12th exercise 31.2 also contains solved questions which cannot be found in the NCERT textbooks.

The RD Sharma class 12th exercise 31.2 provides helpful tips to solve questions in easy methods which cannot be taught in any school.

The RD Sharma class 12 chapter 31 exercise 31.2 is also helpful in solving homeworks as it contains solved questions and tips.

**RD Sharma Chapter-wise Solutions**

- Chapter 1 - Relations
- Chapter 2 - Functions
- Chapter 3 - Inverse Trigonometric Functions
- Chapter 4 - Algebra of Matrices
- Chapter 5 - Determinants
- Chapter 6 - Adjoint and Inverse of a Matrix
- Chapter 7 - Solution of Simultaneous Linear Equations
- Chapter 8 - Continuity
- Chapter 9 - Differentiability
- Chapter 10 - Differentiation
- Chapter 11 - Higher Order Derivatives
- Chapter 12 - Derivative as a Rate Measurer
- Chapter 13 - Differentials, Errors and Approximations
- Chapter 14 - Mean Value Theorems
- Chapter 15 - Tangents and Normals
- Chapter 16 - Increasing and Decreasing Functions
- Chapter 17 - Maxima and Minima
- Chapter 18 - Indefinite Integrals
- Chapter 19 - Definite Integrals
- Chapter 20 - Areas of Bounded Regions
- Chapter 21 - Differential Equations
- Chapter 22 - Algebra of Vectors
- Chapter 23 - Scalar Or Dot Product
- Chapter 24 - Vector or Cross Product
- Chapter 25 - Scalar Triple Product
- Chapter 26 - Direction Cosines and Direction Ratios
- Chapter 27 - Straight Line in Space
- Chapter 28 - The Plane
- Chapter 29 - Linear programming
- Chapter 30- Probability
- Chapter 31 - Mean and Variance of a Random Variable

1. Can students of class 12 also use the RD Sharma solutions?

Yes, students of class 12th can use the RD Sharma solutions for better practice and to score good in boards and competitive exams.

2. How is RD Sharma class 12th solution helpful for me?

It can be beneficial in every way because the RD Sharma book has numerous practice questions updated according to the latest syllabus; this is not offered in most solution books. These solutions are the best answer key for clarifying their doubts.

3. How can a student access the RD Sharma solutions for class 12 Maths from the Career360 website?

Accessing the Solutions of RD Sharma solutions for class 12 books is straightforward. All that a student has to do is, visit the Career360 website and type the book's and the chapter’s name to view the answers.

4. Is the RD Sharma solution of the updated version?

Yes, these solutions are the latest version according to the syllabus of CBSE board exams.

5. From where can I download the RD Sharma class 12th solution?

You can download the online PDFs from the Career360 website, which provides you the material free of cost.

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