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Math Help - Poisson process

  1. #1
    Super Member Anonymous1's Avatar
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    Poisson process

    Customers arrive at an ATM at the times of a Poisson process with rate of 10 per hour. Suppose that the amount of money withdrawn on each transaction has a mean of $30 and a standard deviation of $20. Find the mean and standard deviation of the total withdrawals in 8 hours.
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  2. #2
    Member Focus's Avatar
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    Let N=(N_t:t \geq 0) be your Poisson process and X_1,X_2,... be i.i.d. withdrawal distributions (mean 30 and var 20).

    You are looking for \sum_{i=1}^{N_8} X_i.

    A hint nice hint is that \mathbb{E}[\mathbb{E}[X|Y]]=\mathbb{E}[X].
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