# RD Sharma Solution CLass 12 Mathematics Chapter 32 Mean and Variance of  a Random Variable

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

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22

Solution 22

Question 23

Solution 23

Question 24

Solution 24

Question 25

Solution 25

Question 26

Solution 26

Question 27

Solution 27

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

Question 29

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

(i) Determine the value of k

(ii) Determine P (X  2) and P b(X > 2)

(iii) Find P (X  2) + P(X > 2)

Solution 29

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

Question 1

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

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

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

Solution 9

Question 10

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 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22

Solution 22

Question 23

Solution 23

Question 24

Solution 24

Question 25

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 25

Question 26

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 26

Question 27

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 27

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

## 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

Solution 1

Correct option: (d)

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 0.1 0.2 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)

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)

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)

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)

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)

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)

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)

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.

Solution 9

Correct option: (c)

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

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