If necessary consult a list of formulas Ex Varx Let be a ran

(If necessary, consult a list of formulas.)

E(x)=

Var(x)

Let be a random variable with the following probability distribution: Value of 30 0.10 40 0.45 50 0.10 60 0.35 Find the expectation and variance of . (If necessary, consult a list of formulas.) E(x)= Var(x)

Solution

Consider the table

x   P(x)   x P(x)   x^2 P(x)
30   0.1   3   90
40   0.45   18   720
50   0.1   5   250
60   0.35   21   1260
          
Total       47   2320

Thus,

E(x) = 47 [answer]

Var(X) = E(x^2) - E(x)^2 = 2320 - 47^2 = 111 [answer]