Question

Let X be a random variable with the following probability distribution: Value x of X 40 50 60 70 80 P(X=x) 0.05 0.25 0.10 0.30 0.30 Find the expectation E (X) and variance Var (X) of X. (If necessary, consult a list of formulas.) x 6 ? E (x) = 0 Var(x) = 0

Answer 1

Solution :

x	P(x)	x * P(x)	x2 * P(x)
40	0.05	2	80
50	0.25	12.5	625
60	0.1	6	360
70	0.3	21	1470
80	0.3	24	1920

Mean = E(X) = $\sum$ X * P(X) = 24   

Variance = $\sum$ X ² * P(X) - $\mu$ ² = 1920 - 24² = 164.75