Question

Give the probability distribution for X:

x 0 1 2 3
f(x) 1/4 1/8 1/2 1/8

Find Var.

Answer 1

Answer:

Var(x)=1

Step-by-step explanation:

x p(x)         x² x*p(x) x²*p(x)

0 1/4     0 0         0

1 1/8     1 1/8             1/8

2 1/2     4 1           2

3 1/8     9 3/8            9/8

Total                      3/2              13/4

The required variance can be computed as

Var(x)=sumx²*p(x)-(sum(x*p(x)))²

Var(x)=13/4-(3/2)²

Var(x)=13/4-9/4

Var(x)=4/4

Var(x)=1

Thus, the required variance is 1.