A die is tossed thrice. A success is 1 or 6 on a toss. Find the mean and variance of successes.
Using Bernoulli’s Trial we have,
P(Success=x) = nCx.px.q(n-x)
x=0, 1, 2, ………n and q = (1-p), n =3
p = 2/6 = 1/3, q = 4/6 = 2/3
P(x = 0) = P (no success) = P (all failures) = (
)(
)(
)= 
P(x = 1) = P (1 success and 2 failures) = 3C1(
)1(
)2 = 
P(x = 2) = P (2 success and 1 failure) =3C2(
)2(
)1 = 
P(x = 3) = P (all 3 success) = 3C3(
)3(
)0 = 
∴ The probability distribution of the random variable x is -
x : 0 1 2 3
P(x) : 
x1 p1 p1x1 p1x12
0 
0 0
1 
2 
3 
1 
Mean μ = Σp1x1 = 1
Variance = 
2 = Σp1x12 - μ
⇒ 5/3 - 1/1
⇒ 2/3
1