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15 November, 21:27

After a big win at the slot machine, a gambler stuffs his pockets with quarters and walks down the Las Vegas strip. Unfortunately, there is a hole in one pocket and the coins drop out randomly, at a rate of 5 per 50 meters. If you follow the gambler for 100 meters, what is the probability mass function for the number of quarters you find on the sidewalk, head up?

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  1. 15 November, 21:36
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    Step-by-step explanation:

    Given That:-

    After a big win at the slot machine, a gambler stuffs his pockets with quarters and walks down the Las Vegas strip. Unfortunately, there is a hole in one pocket and the coins drop out randomly, at a rate of 5 per 50 meters.

    A gambler stuffs his pockets with quarters and walks down the Las Vegas strip.

    Unfortunately, there is a hole in one pocket and the coins drop out randomly, at a rate of 5 per 50 meters.

    λ = rate of finding a quarter = 5 (for 50 meters)

    Now, for 100 meters, λ = 5 x 2 = 10.

    If X = random variable denoting no. of quarter found on sidewalk, head up.

    X - possion (λ = 10).

    There the probability mass function = P (X = x) = e^{-λ} x λ^{x} / {x!}

    = e^{-10} x {10^{x} / {x!}; x = 0, 1, 2, ... = is the probability mass function for the number of quarters you find on the sidewalk, head up.
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