Question

Let the random variable X have a discrete uniform distribution on the integers 6 ≤ x ≤ 12. Determine the mean, μ, and variance, σ2, of X. Round your answers to two decimal places (e.g. 98.76). μ = σ2 =

Answer 1

we know that p.m.f. of discrete uniform distribution is given as

P(X=x) = 1 / n ; x= 1,2,3,4,5,...n

but we have given the range as 6 x 12

so p.m.f. of discrete uniform distribution become as

P(X=x) = 1/7 ; x=6,7,8,9,10,11,12

Therefore

Mean = = (1/7)*6+(1/7)*7 +(1/7)*8 +(1/7)*9 + (1/7)*10 +(1/7)*11 + (1/7)*12

=63/7

Mean = 9

E(x^2) == (1/7)*36+(1/7)*49 +(1/7)*64 +(1/7)*81 + (1/7)*100 +(1/7)*121 + (1/7)*144

  E(x^2) = 85

Now,

Var (x) =      E(x^2) - (mean)^2

var(x) = 85 - ( 9)^2

Var(x) = 4

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Thank You !