Question

Given the following table, answer the questions below.

x	f(x)
0	0.05
1	0.2
2	0.3
3	0.45

a) Find the mean of this probability distribution. Round your answer to one decimal place.

b) Find the standard deviation of this probability distribution. Give your answer to at least 2 decimal places.

Answer 1

Solution:

x	P(X)	x*P(x)	x2	x2* P(x)
0	0.05	0	0	0
1	0.2	0.2	1	0.2
2	0.3	0.6	4	1.2
3	0.45	1.35	9	4.05
Sum	1	2.15	14	5.45

a)

Mean = E(X)

= Summation(x.P(X))

= 2.15

Mean   =  2.15

b)

Now , E(X²) = summation [x² * P(X)] = 5.45

Variance ² = E(X²) - [E(x)]²

= 5.45 - [2.15]²

=  0.8275

Variance ² = 0.8275

Now ,

Standard deviation =   =  0.8275=  0.90967026993 = 0.91

Standard deviation   = 0.91