Suppose you are drawing randomly from three cards: a jack, a queen, and a king. If you draw a jack it pays off 0 dollars, if you draw a queen it pays off 2 dollars, and if you draw a king it pays off 3 dollars. What are the expected value, variance, and standard deviation of your payoff from this game?
Now suppose you draw twice, without replacement (i.e., for the second draw you are only drawing from the remaining two cards). The payoffs are the same as above for both draws. How do you calculate the expected value, variance, and standard deviation of the total payoff from the two draws?
Let's give me a try. From my point of view the cards are uniformly distributed. Therefore
$P(X=x)=\frac{1}{3}$ Expected Value is defined as $\mathbb{E}\left [ X \right ] = \sum_{i=1}^{3}x_{i}p_{i}$.
Plug in the numbers and you will get: 1.66667
By the same way you can compute variance and sdt as well.