VITEEE 2014 Paper

Let x denote the sum of the numbers obtained when two fair dice are rolled.
So, X may have values 2,3,4,5,6,7, 8,9, 10,11 and 12.
P (X = 2) = P (1 , 1) =

1

36

P (X = 3) = P {(1 , 2) , (2 , 1)} =

2

36

P (X = 4) =

3

36

, P (X = 5) =

4

36

;
P (X = 6) =

5

36

; P (X = 7) =

6

36

;
P (X = 8) =

5

36

;
P (X = 9) =

4

36

;
P (X = 10) =

3

36

' P (X = 11)
=

2

36

;
P (X = 12) =

1

36

∴ Probability distribution table is given below

Mean

−

X

= Σ XP (X)
=
=

252

36

= 7
Variance = ΣX2 P (X) -

−

X

2
= - 72
=

1974

36

- 49
=

1974−1764

36

=

210

36

=

35

6

∴ Variance =

35

6

And , SD = √

35

6