Question

1. Consider the following random discrete distribution.

x	x(P)
24	0.25
30	0.15
49	0.30
58	0.10
60	0.20

1. Calculate the mean or the expected value of X

2. Calculate the variance and the standard deviation of the random variable

Answer 1

Solution:

Mean = ∑XP(X)

Variance = ∑ P(X)(X - mean)^2

Standard deviation = Sqrt[∑ P(X)(X - mean)^2]

The calculation table is given as below:

X	P(X)	XP(X)	P(X)(X - mean)^2
24	0.25	6	90.25
30	0.15	4.5	25.35
49	0.3	14.7	10.8
58	0.1	5.8	22.5
60	0.2	12	57.8
Total	1	43	206.7

Part a

Mean = 43

Part b

Variance = 206.7

Standard deviation = Sqrt(206.7) = 14.37706507

Standard deviation = 14.37706507