<p>Each customer who enters a clothing store will purchase a suit with probabili

Question

<p>Each customer who enters a clothing store will purchase a suit with probability of 0.5. If the number of customers entering the store is Poisson distributed with mean 2. Let X be the total number of suits the store sells. Find E(X) and Var(X).<br /><br /><br />I did this:<br /><br />E(x) =&#160;&#931; E(XIY=k)*P(Y=k) and sum is from 0 to infinity.</p>
<p>E(x²) = &#931; E(X²IY=k)*P(Y=k) and sum is from 0 to infinity.</p>
<p>I am stuck on how to evaluate those equations. Please help.</p>

Explanation / Answer

Let Y = number of customers in store, which is Poisson with mean 2 So E(Y) = 2 and Var(Y) = 2 Since X = 0.5Y, E(X) = 0.5*2 = 1 and Var(Y) = 0.5^2 * Var(X) = 0.25*2 = 0.5

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