Question

A random variable x has the following probability distribution. Determine the standard deviation of x.

x	f(x)
0	0.05
1	0.1
2	0.3
3	0.2
4	0.35

A random variable x has the following probability distribution. Determine the expected value of x.

x	f(x)
0	0.11
1	0.04
2	0.3
3	0.2
4	0.35

QUESTION 2

1. A random variable x has the following probability distribution. Determine the variance of x.

   x	f(x)
   0	0.02
   1	0.13
   2	0.3
   3	0.2
   4	0.35

Answer 1

Following table shows the calculations:

x	f(x)	x*f(x)	x^2*f(x)
0	0.05	0	0
1	0.1	0.1	0.1
2	0.3	0.6	1.2
3	0.2	0.6	1.8
4	0.35	1.4	5.6
Total		2.7	8.7

The standard deviation is

------------------------------

x	f(x)	x*f(x)
0	0.11	0
1	0.04	0.04
2	0.3	0.6
3	0.2	0.6
4	0.35	1.4
Total		2.64

The expected value is

----------------------------

x	f(x)	x*f(x)	x^2*f(x)
0	0.02	0	0
1	0.13	0.13	0.13
2	0.3	0.6	1.2
3	0.2	0.6	1.8
4	0.35	1.4	5.6
Total		2.73	8.73

The variance is