## Expected Value

The expected value of a discrete random variable X with possible values of X

_{1}, X

_{2}, ..., X

_{k}with probabilities of p

_{1}, p

_{2}, ..., p

_{k}respectively, the expected value of X is given by:

Properties of Expected Value:

- E(X + c) = E(X) + c (for constant c)
- E(X + Y) = E(X) + E(Y)
- E(cX) = cE(x) (for constant c)

If a raffle ticket offers a first prize
of $1000 and a second prize of $500 with probabilities of winning at
0.01 and 0.03 respectively, what be a fair price to pay for a ticket?

Solution:

Expected Value of Raffle Ticket

= $1000 (0.01) + $500 (0.03)

= $10 + $15

= $25

= $1000 (0.01) + $500 (0.03)

= $10 + $15

= $25