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1 May, 14:53

Cars enter a car wash at a mean rate of 2 cars per half an hour. What is the probability that, in any hour, exactly 2 cars will enter the car wash? Round your answer to four decimal places. Poisson Distribution

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  1. 1 May, 17:49
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    X1: # cars enter for wash a half hour duration.

    X2: # cars enter for wash the next half hour duration.

    X1 and X2 are independent Poisson variates (iid) with common mean 2.

    Then X=X1+X2 : # cars enter for wash in one hour duration is a Poisson variate with mean m = 2+2

    pmf is p (x) = e^-m m^x / x!, x=0, 1, 2, ...

    P[more than 3 cars] = 1 - P[3 or less cars]

    = 1 - [p (0) + p (1) + p (2) + p (3) ]
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