If the range of X is the set {0,1,2,3,4,5,6,7,8} and P(X=x) as defined in the following table:

x	0	1	2	3	4	5	6	7	8
P(X=x)	0.06528	0.3870	0.03062	0.0968	0.06913	0.0968	0.04846	0.01252	0.1935

Determine the mean and variance.

Solution:

Mean:

E(x) = ∑ xᵢp(xᵢ)

∑ xᵢp(xᵢ) = 1(0.3870) + 2(0.038062) + 3(0.0968) + 4(0.06913) + 5(0.0968) + 6(0.04846) + 7(0.01252) + 8(0.1935)

∑ xᵢp(xᵢ) = 3.43672

Mean = 3.43672

Variance:

Variance = E(x²) - [E(x)]²

E(x²) = ∑ x²ᵢp(xᵢ)

∑ x²ᵢp(xᵢ) = 1²(0.3870) + 2²(0.038062) + 3²(0.0968) + 4²(0.06913) + 5²(0.0968) + 6²(0.04846) + 7²(0.01252) + 8²(0.1935)

∑ x²ᵢp(xᵢ) = 19.6488

∴ Variance = 19.6488 - (3.43672)² = 7.837755

x	0	1	2	3	4	5	6	7	8
P(X=x)	0.06528	0.3870	0.03062	0.0968	0.06913	0.0968	0.04846	0.01252	0.1935

Determine the mean and variance.

Summary:

Mean and Variance of the given table are 3.43672 and 7.837755 respectively.