Given the following discrete uniform probability distribution, find the expected value and standard deviation of the...

Given the following discrete uniform probability distribution, find the expected value and standard deviation of the random variable. Round your final answer to three decimal places, if necessary.

Probability Distribution
x	0	1	2	3	4	5	6	7	8	9	10
P(X=x)	1/11	1/11	1/11	1/11	1/11	1/11	1/11	1/11	1/11	1/11	1/11

Expert Solution

Solution:

x	P(x)	x * P(x)	x² * P(x)
0	0.09	0.301	0
1	0.09	0.09	0.09
2	0.09	0.18	0.36
3	0.09	0.27	0.81
4	0.09	0.36	1.44
5	0.09	0.45	2.25
6	0.09	0.54	3.24
7	0.09	0.63	4.41
8	0.09	0.72	5.76
9	0.09	0.81	7.29
10	0.09	0.9	9
	1	5.251	34.65

Mean = = x P (x ) = 5.251

Standard deviation = = x² P (x ) - ( )²

= 34.65- ( 5.251 )²

= 34.65 - 27.57

= 7.08

= 2.661

orchestra answered 1 year ago

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