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sattari [20]
3 years ago
7

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

able. 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
Mathematics
1 answer:
katovenus [111]3 years ago
3 0

The expected value is

E[X]=\displaystyle\sum_xx\,P(X=x)=\frac1{11}\sum_{x=0}^{10}x=\dfrac{0+1+\cdots+9+10}{11}=\dfrac{55}{11}=\boxed{5}

The standard deviation is the square root of the variance, which is

V[X]=E[(X-E[X])^2]=E[X^2]-E[X]^2

where

E[X^2]=\displaystyle\sum_xx^2\,P(X=x)=\frac1{11}\sum_{x=0}^{10}x^2=\dfrac{0^2+1^2+\cdots+9^2+10^2}{11}=\dfrac{385}{11}=35

so that

V[X]=35-5^2=10

making the standard deviation

\sqrt{V[X]}=\sqrt{10}\approx\boxed{3.16}

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