RD SHARMA Solutions for Class 12-science Maths Chapter 32 - Mean and variance of a random variable

Page / Exercise

Chapter 32 - Mean and variance of a random variable Exercise Ex. 32.1

Question 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 13

 
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable
Question 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 26

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 26

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 28

Four balls are to be drawn without replacement from a box containing 8 red and 4 white balls. If X denotes the number of red balls drawn, find the probability distribution of X.

Solution 28

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable 

Question 29

The probability distribution of a random variable X is given below:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable 

(i) Determine the value of k

(ii) Determine P (X Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable 2) and P b(X > 2)

(iii) Find P (X Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable 2) + P(X > 2)

Solution 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable 

Chapter 32 - Mean and variance of a random variable Exercise Ex. 32.2

Question 1(i)

Find the mean and standard deviation of each of the following probability distributions:

xi : 2 3 4

pi : 2.2 0.5 0.3

Solution 1(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable 

Question 1(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 1(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 1(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 1(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 1(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 1(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 1(v)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 1(v)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 1(vi)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 1(vi)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 1(vii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 1(vii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 1(viii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 1(viii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 1(ix)

Find the mean and standard deviation of each of the following probability distributions:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable 

Solution 1(ix)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable 

Question 2

A discrete random variable X has the probability distribution given below:

X : 0.5 1 1.5 2

P(X) : k k2 2k2 k

(i) Find the value of k.

(ii) Determine the mean of the distribution.

Solution 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable 

Question 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random VariableRd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 17

Three cards are drawn at random (without replacement) from a well shuffled pack of 52 cards. Find the probability distribution of number of red cards. Hence find the mean of the distribution.

Solution 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 18

An urn contains 5 are 2 black balls. Two balls are randomly drawn, without replacement. Let X represent the number of black balls drawn. What are the possible values of X? Is X a random variable? If yes, find the mean and variance of X.

Solution 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable 

Question 19

Two numbers are selected at random (without replacement) from positive integers 2,3,4,5, 6 and 7. Let X denote the larger of the two number obtained. Find the mean and variance of the probability distribution of X.

Solution 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable 

Chapter 32 - Mean and variance of a random variable Exercise MCQ

Question 1

If a random variable X has the following probability distribution:

X:

0

1

2

3

4

5

6

7

8

P(X):

a

3a

5a

7a

9a

11a

13a

15a

17a

then the value of a is

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable 

Solution 1

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable 

Question 2

A random variable X has the following probability distribution:

X:

1

2

3

4

5

6

7

8

P(X):

0.15

0.23

0.12

0.10

0.20

0.08

0.07

0.05

 

For the event E = {X:X is a prime number}, F = {X:X F) is

a. 0.50

b. 0.77

c. 0.35

d. 0.87

 

Solution 2

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable 

Question 3

A random variable X takes the values 0, 1, 2, 3 and its mean is 1.3. If P(X=3)=2 P(X=1) and P (X=2)=0.3, then P(X=0) is

a. 0.1

b. 0.2

c. 0.3

d. 0.4

Solution 3

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable 

Question 4

A random variable has the following probability distribution:

X=xi:

0

1

2

3

4

5

6

7

P(X=xi):

0

2p

2p

3p

P2

2p2

7p2

2p

The value of P is

a. 1/10

b. -1

c. -1/10

d. 1/5

 

Solution 4

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable 

 

Question 5

If X is a random -variable with probability distribution as given below:

X=xi:

0

1

2

3

P(X=xi):

k

3k

3k

k

The value of k and its variance are

a. 1/8, 22/27

b. 1/8, 23/27

c. 1/8, 24/27

d. 1/8, 3/4

 

Solution 5

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable 

Question 6

The probability distribution of a discrete random variable X is given below:

X:

2

3

4

5

P(X):

5/k

7/k

9/k

11/k

The value of E(x) is

a. 8

b. 16

c. 32

d. 48

 

Solution 6

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

NOTE: Question is modified. 

Question 7

For the following probability distribution:

X:

-4

-3

-2

-1

0

P(X):

0.1

0.2

0.3

0.2

0.2

 

The value of E(X) is

a. 0

b. -1

c. -2

d. -1.8

 

Solution 7

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable 

 

Question 8

For the following probability distribution:

X:

1

2

3

4

P(X):

1/10

1/5

3/10

2/5

The value of E(X2) is

a. 3

b. 5

c. 7

d. 10

Solution 8

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable 

Question 9

Let X be a discrete random variable. Then the variance of X is

a. E(X2)

b. E(X2) + (E(X))2

c. E(X2) - (E(X))2

d. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable 

Solution 9

Correct option: (c)

Variance of discrete random variable is always E(X2) - (E(X))2

 

Chapter 32 - Mean and variance of a random variable Exercise Ex. 32VSAQ

Question 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Question 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable

Solution 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Mean And Variance Of A Random Variable