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					Section 11.6
Expectation
Definition of Expectation

   Let S1, S2, S3, …, Sn be the possible outcomes of
    an experiment and let P(S1),P(S2),P(S3),…, P(Sn)
    be the probabilities of those outcomes. Then the
    expectation of the experiment is
    P(S1) · S1 + P(S2) · S2 + P(S3) · S3 + … + P(Sn) · Sn
Examples (Page 753)
   Example One of the wagers in roulette is to
    place a bet on one of the numbers from 0 to
    36 or on 00. If that number comes up, the
    player wins 35 times the amount bet (and
    keeps the original bet). Suppose a player
    bets $1 on a number. What is the player’s
    expectation?
Examples (Page 754)
   Example In roulette it is possible to place a
    wager that one of the numbers between 1
    and 12 (inclusive) will come up. If it does, the
    player wins twice the amount bet. Suppose a
    player bets $5 that a number between 1 and
    12 will come up. What is the player’s
    expectation?
Examples (Page 755)
   Example According to some data, the
    probability that a 27-year-old will die within
    one year is about 0.001. Suppose that the
    premium for a one year, $25,000 life
    insurance policy for a 27-year-old is $32.
    What is the insurance company’s expectation
    for this policy?
Examples (Page 755)
   Example According to some data, the
    probability that a 51-year-old will die within
    one year is about 0.005. Suppose that the
    premium for a one year, $10,000 life
    insurance policy for a 51-year-old is $45.
    What is the insurance company’s expectation
    for this policy?
   Example 3 (Page 756) A road construction
    company bids on a project to build a new
    highway. The company estimates its

    potential profit as show in the table below.
    What is the expectation for the company?

				
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