Question

Please help find the expectation and the variance

Answer 1

The values of the expectation, E(X) and Variance, Var(X) are : 9 and 199 respectively .

The expectation, E is calculated using the relation:

• E(X) = ∑x*p(x)

E(X) = (-10*0.30) + (0*0.15) + (10*0.20) + (20*0.05) + (30*0.30)

E(X) = 9

B.)

The expected variance ;

• Var(X) = ∑x² *p(x) - E(X)²

∑x²*p(x) = (-10^2*0.30) + (0^2*0.15) + (10^2*0.20) + (20^2*0.05) + (30^2*0.30) = 280

Var(X) = 280 - 9²

Var(X) = 280 - 81

Var(X) = 199