Question

Find the variance of the following data. Round your answer to one decimal place. x 3 4 5 6 7 8 P(X=x) 0.1 0.1 0.1 0.2 0.2 0.3

Answer 1

x	3	4	5	6	7	8
P (X = x )	0.1	0.1	0.1	0.2	0.2	0.3

μ = E(X) = ∑ x ∙ P(X=x)

        = ( 3 ∙ 0.1)    +   ( 4∙ 0.1)   +   (5∙ 0.1) + (6 ∙ 0.2 )   +   ( 7 ∙ 0.2)   + ( 8∙ 0.3)

        = 0.3 + 0.4   + 0.5 + 1.2 +   1.4 + 2.4

      μ = E(X) = 6.2

E(X²) = ∑ x² ∙ P(X=x)

                 = ( 9 ∙ 0.1)    +   ( 16∙ 0.1)   +   (25∙ 0.1) + ( 36 ∙ 0.2 )   +   ( 49 ∙ 0.2)   + ( 64 ∙ 0.3)

                 = 0.9 + 1.6 + 2.5 + 7.2   + 9.8 +   19.2

E(X²) = 41.2

Variance is given by;

V(X) = E(X²) - [ E(X) ]²

         = 41.2 - [ 6.2 ]²

         = 41.2 - 38.44

       V(X) = 2.76