Question

The following table provides a probability distribution for the random variable y. y f(y)

3 0. 20

5 0. 20

7 0. 30

9 0. 30

a. Compute E(y) (to 1 decimal).

b. Compute Var(y) and σ (to 2 decimals).

Var(

y)

σ

Answer 1

Solution:

Given that,

y	f(y)	y*f(y)	y^2*f(y)
3	0.2	0.6	1.8
5	0.2	1	5
7	0.3	2.1	14.7
9	0.3	2.7	24.3
Sum=	1	6.4	45.8

Mean :

E(Y) = Y * f(Y)

= 6.4

Variance :

V(Y) = Y² * P(Y) - ()²

= 45.8 - ( 6.4 )²

= 4.84

Standard deviation:

= Y² * f(Y) - ()²

= V(y)

= 4.84

= 2.20