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Five balls numbered $0,2,4,6,8$ are placed in a bag. After the balls are mixed, one of them is selected, its number is noted, and then it is replaced. If this experiment is repeated many times, find the variance and standard deviation of the numbers on the balls.

I choose $X=0,2,4,6,8$, and hence $f(0)= f(2)=f(4)=f(6)=f(8)= \frac15$. So I think to use the formula $\sigma^2=\mu_2-\mu^2$ to find variance where $\mu=\sum{xf(x)}$ and $\mu_2=\sum{x^2f(x)}$. This is what i think for this question!

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    Yes, this is the way to do it; but it seems your typesetting is off. Do you mean to write $\sigma^2= \sum x^2f(x)-(\sum xf(x))^2$?2011-12-27
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    @DavidMitra I and Srivatsan fixed the typesetting. Hope that's what OP intended.2011-12-27
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    I find this question a bit puzzling (which presumably is the question-setter's fault, not neemy's). Would the mean and variance be any different if the experiment is _not_ repeated many times? The question _does_ ask for the variance and standard deviation of the _numbers_ which could well mean: In $n$ experiments, the numbers $0,2,4,6,8$ were found to have occurred $n_0, n_2, n_4, n_6,$ and $n_8$ times where $n_0+n_2+n_4+n_6+n_8=n$. What is the variance and standard deviation? etc.2011-12-27

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