Probability - expected value

Question

What is your expected value for a game whose probabilities and outcomes are given in the following table?

0.2	You win 1.4 times your wager.
0.4	You win your wager.
0.2	You lose 2 times your wager.
0.2	You win nothing.

Answer 1

Let's think about the case where we wager one dollar.

For an expected value we take the mean result by summing over all the possible results multiplied by their probability of occurring. So, our math looks like this:

E[x] = (0.2)($1.4) + (0.4)($1) + (0.2)($-2) + (0.2)($0),

where E[x] is the expected winnings from the betting scheme.

E[x] = ($0.7) + ($0.4) - ($0.4)

E[x] = $0.7.

If I were writing this up as a homework problem I would carry through the variable of the wager.

Let me know if this makes sense!