(solution) Let be a random variable with the following probability

(solution) Let be a random variable with the following probability

Let be a random variable with the following probability distribution:

Value x of x                    PX=X

0                                        .05

10                                      .35

20                                     .15

30                                     .40

40                                      .05 Find the expectation X and variance X of X .

x p
0
10
20
30
40 E(X)
var(X) x^2
0.05
0.35
0.15
0.4
0.05
20.5
114.75 x*p
0
100
400
900
1600 x^2*p
0
3.5
3
12
2
20.5 0
35
60
360
80
535