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

Var(x)=1

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.