In tossing a die once, the sample space is given by
S={1,2,3,4,5,6}.
∴ P(getting an even number)=
3
6
=
1
2
,
P(getting an odd number)=
3
6
=
1
2
.
As given, X takes the value 0 or 1.
P(X=0)=P(getting an odd number)=
1
2
.
P(X=1)=P(getting an even number)=
1
2
.
Thus, the probability distribution of X is given by
∴ mean,μ=Σxipi=(0×
1
2
)+(1×
1
2
)=
1
2
.
Variance, σ2=Σx
2
i
pi-μ2
(0×
1
2
)+(1×
1
2
)-(
1
2
)2=(
1
2
-
1
4
)=
1
4
.
