Question

Consider the discrete random variable XX given in the table below. Calculate the mean, variance, and standard deviation of XX.

XX	6	7	8	12	15
P(XX)	0.11	0.13	0.07	0.11	0.58

μμ =
σ2σ2 =
σσ =


What is the expected value of XX?

Answer 1

Solution:

Given that,

X	P(X)	X*P(X)	X^2*P(X)
6	0.11	0.66	3.96
7	0.13	0.91	6.37
8	0.07	0.56	4.48
12	0.11	1.32	15.84
15	0.58	8.7	130.5
Sum=	1	12.15	161.15

Mean :

= X * P(X)

= 12.15

Variance :

= X² * P(X) - ()²

= 161.15 - ( 12.15 )²

= 13.5275

= 13.53

Standard deviation:

= X² * P(X) - ()²

= 13.5275

= 3.6780

= 3.68

The expected value of X is,

E(X) = = X * P(X)

= 12.15