Download Chapter 5.2: Expectation

Chapter 5.2
Expectation
Expectation
 Another concept related to the mean for a probability
distribution is that of expected value or expectation.
 Expected value is used in various types of games of
chance, in insurance, and other areas, like decision
theory.
Expectation
 The expected value of a discrete random variable of a
probability distribution is the theoretical average of
the variable.
 Formula:   E ( X )  X  P( X )
 E(X) represents the expected value
Winning Tickets
 One thousand tickets are sold at $1 each for a
television valued at $350. What is the expected value
of the gain if you purchase one ticket?
Special Die
 A special six-sided die is made in which 3 sides have
six spots, two sides have four spots, and one side has
one spot. If the die is rolled find the expected value of
the number of spots that will occur.
Bond Investment
 A financial adviser suggests that his client select one
of two types of bonds in which to invest $5000. Bond
X pays a return of 4% and has a default rate of 2%.
Bond Y has a 2.5% return and a default rate of 1%. Find
the expected rate of return and decide which bond
would be a better investment. (When the bond
defaults, the investor loses all the investment)
Chuck-A-Luck
 Chuck-a-luck This game (found in fairgrounds) is
played by rolling 3 dice and betting on a number
between 1 and 6. You win your bet multiplied by the
number of times your chosen value appears on the
three dice. For example if you bet $1 on 5 and roll 4; 5;
5 you win $2. Find the expected value of betting $1 on
4.
Las Vegas Roulette
 At the Las Vegas roulette (with 38 numbers,
0,00,1,2,3, etc) you can do various bets (let's say the
bet size is $1). Find the expected value of betting on
each of the following
 1. Bet on red (or black) and a successful bet pays you
$1.
 2. Bet on a number and a successful bet pays you $35.
 3. Bet on the first (or the second, the third) dozen of
numbers a successful bet pays you $2.
Try it!
 Applying the concepts, Pg. 274 #1-7