Question

The table below shows the probability distribution for x, the number that shows up when a loaded die is rolled:

X	P(X)
1	0.12
2	0.10
3	0.12
4	0.14
5	0.15
6	0.37

a) Find the mean of the distribution.

b) Find the standard deviation of the distribution.

Answer 1

Solution:

x	P(x)	x * P(x)	x2 * P(x)
1	0.12	0.12	0.12
2	0.1	0.2	0.4
3	0.12	0.36	1.08
4	0.14	0.56	2.24
5	0.15	0.75	3.75
6	0.37	2.22	13.32
Sum	1	4.21	20.91

Mean = X * P(X)

= 4.21

Standard deviation =

=X 2 * P(X) - 2

=  20.91 - (4.21)2 = 3.1859

Standard deviation = = 1.7849