Question

Find the mean and standard deviation of the random variable X with the following distribution:

X 0 1 2 3 4

Probability 0.1 0.2 0.3 0.3 0.1

	I.	1.8, 1.29
	II.	1.00, 1.00
	III.	2.1, 1.135
	IV.	2.1, 1.29

Answer 1

Solution:

x	P(x)	x * P(x)	x2 * P(x)
0	0.1	0	0
1	0.2	0.2	0.2
2	0.3	0.6	1.2
3	0.3	0.9	2.7
4	0.1	0.4	1.6
Sum	1	2.1	5.7

Mean = X * P(X)

= 2.1

Standard deviation =

=X 2 * P(X) - 2

=  5.7 - (2.1)2 = 1.29

Standard deviation = = 1.135

option III is correct 2.1 , 1.135