Question

A fair cubical die is thrown 36 times, and the random variable X represents the number of 6’s obtained. Find:- The mean and variance of X. ( < − ).

Answer 1

Answer:

2.15

Step-by-step explanation:

Let X denote the event of getting twice the number. Then, X can take the values 1,2,3,4,5 and 6.

Thus, the probability distribution of X is given by

x P(X)

1

36

11

2

36

9

3

36

7

4

36

5

5

36

3

6

36

1

x

i

p

i

p

i

x

i

p

i

x

i

2

1

36

11

36

11

36

11

2

36

9

36

18

1

3

36

7

36

21

36

63

4

36

5

36

20

36

80

5

36

3

36

15

36

75

6

36

1

36

6

1

∑p

i

x

i

=

36

91

=2.5 ∑p

i

x

i

2

=8.4

⇒ Mean =∑p

i

x

i

=6.25

⇒ Variance =∑p

i

x

i

2

−(Mean)

2

=8.4−6.25

=2.15