Find Variance and Standard Deviation 
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! 
 A: Yes, this is the way to do it. 
But the problem is stated a little imprecisely. You should write something like: "Let the random variable $X$ be the number that appears on the selected ball. Find the variance and standard deviation of $X$".
The variance of a random variable $X$, denoted by $\sigma^2_{  X}$, can be calculated using the formula
$$
\sigma^2_X=\Bbb E(X^2)-[\Bbb E(X)]^2;$$
which, in the discrete case, gives
$$\sigma^2_X=\sum_i x_i^2 p_X(x_i) -\bigl[\,\sum_i x_i  p_X(x_i) \,\bigr]^2
$$
where $p_X$ is the probability mass function of $X$ and the $x_i$ are the distinct values that $X$ takes.
In your problem, as you state, $X$ takes the values $0, 2, 4, 6, 8$ with equal probabilities $1/5$. So, $p_X(i)=1/5$ for $i=0,2,4,6, 8$, and:
$$
\sigma_X^2= \sum_{i\in\{0,2,4,6,8\}} i^2\cdot{\textstyle{1\over 5}}
- \Bigl[ \sum_{i\in\{0,2,4,6,8\}} i \cdot{\textstyle{1\over 5}}\Bigr]^2.
$$
I'll leave the actual computation to you.
Of course, the standard deviation of $X$ is just the square root of the variance.
