Expected Value
The expected value of a discrete random variable X with possible values of X1, X2, ..., Xk with probabilities of p1, p2, ..., pk 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