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