The question is as follows:
Draw 4 cards from a deck of 54 cards (with 2 jokers), what is the expected value of the 4 cards? Assume the value of a J is 11, Q is 12 and K is 13, a joker is 100.
The answer provided is:
We need to compute:
$ \quad \mathbb{E}(X_1+X_2+X_3+X_4) = \mathbb{E}(X_1)+ \mathbb{E}(X_2)+ \mathbb{E}(X_3)+ \mathbb{E}(X_4)$ = $4\mathbb{E}(X_1)$
My question is why do we have $\quad \mathbb{E}(X_1)=\mathbb{E}(X_2)=\mathbb{E}(X_3)=\mathbb{E}(X_4)$?
If we draw one card each time and with replacement, we draw the next one, I can understand the equation. But if we draw four times consecutively without replacement, do we still have the equal expectations for four times? Why? Thanks!