Mathematics, 03.03.2020 17:30, bellam302
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
Answers: 2
![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}](/tpl/images/0532/2434/3d543.png)
![V[X]=E[(X-E[X])^2]=E[X^2]-E[X]^2](/tpl/images/0532/2434/9ca41.png)
![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](/tpl/images/0532/2434/de66f.png)
![V[X]=35-5^2=10](/tpl/images/0532/2434/1c909.png)
![\sqrt{V[X]}=\sqrt{10}\approx\boxed{3.16}](/tpl/images/0532/2434/62155.png)
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