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Math Help - Expected Value

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    Expected Value

    QUESTION : With an infinite number of stores, half charging $1 and half charging $2. You decide to check three stores randomly and buy from a store which has the minimum of the three prices checked. What is the expected value of the price you will pay?
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    Quote Originally Posted by timk19 View Post
    QUESTION : With an infinite number of stores, half charging $1 and half charging $2. You decide to check three stores randomly and buy from a store which has the minimum of the three prices checked. What is the expected value of the price you will pay?
    $2, $2, $2 => you pay $2. Pr($2, $2, $2) = (1/2)^3 = 1/8.

    At least one $1 store => you pay $1. Pr(at least one $1 store) = 7/8.

    Therefore ......
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    RE:

    Isn't the expected value the mean? Shouldn't the expected value be represented as a dollar amount?
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    Quote Originally Posted by timk19 View Post
    Isn't the expected value the mean? Shouldn't the expected value be represented as a dollar amount?
    Expected Value could be considered a weighted average, but it's usually not the mean of a set of numbers. It is calculated as the sum of n \cdot P(n) over all possible values of n. In the case of your problem, there is a 1/8 probability you will have all $2 stores and have to pay $2, and a 7/8 probability that at least one of the three stores will be a $1 store and you have to pay $1. No other values besides $1 and $2 are possible, so the Expected Value is (1/8)*2 + (7/8)*1. In this problem, it makes sense to give this number a dollar sign.
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    Quote Originally Posted by timk19 View Post
    Isn't the expected value the mean? Shouldn't the expected value be represented as a dollar amount?
    If you understand how to calculate an expected value I would have thought my post gave everything necessary for doing the calculation.
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    Thumbs up re:

    Perfect, thank you.
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