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Homework Help: Multivariate probability distributions?

  1. Nov 27, 2008 #1
    1. The problem statement, all variables and given/known data
    Let Y be the number of customers entering a ABC bank in a day. It is known that Y has a Poisson distribution with some unknown mean lambda. Suppose that 1% of the customers entering the branch in a day open a new ABC bank account. Find the mean and variance of the number of customers who open a new ABC bank account in a day.

    2. Relevant equations
    3. The attempt at a solution

    Just based on past experience, I THINK this is related to multivariate distributions and PROBABLY would use the fact E[E(Y|X)]=E(Y). But I am not sure how to define the random variables properly...

    Can someone explain?

    Thanks for any help!
  2. jcsd
  3. Nov 27, 2008 #2


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    Science Advisor

    No, it is NOT a multivariate distribution- there is only the single variable, the number of customers. You are asked for the mean and variance of 0.01Y where Y is Poisson distributed.

    If [itex]\sum yP(y)= \lambda[/itex], what is [itex]\sum 0.01 yP(y)[/itex]?
  4. Nov 28, 2008 #3
    OK, so this is actually a univariate problem...

    Let Z=number of customers who open a new ABC bank account in a day
    Then our job is to find E(Z) and Var(Z)?

    Or is our job to find E(0.01Y) and Var(0.01Y) where Y~Poisson(lambda)?

    Thank you!
  5. Dec 1, 2008 #4
    So Z = 0.01 Y, we need to find E(Z) and Var(Z)
    Var(Z)=Var(0.01Y)=(0.01^2) Var(Y)=0.0001*lambda

    Am I right? Is to any way to find lambda?
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