Equivalence of two expected value terms and the distribution of its parameters

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Problem:

"The number of breakdowns $Y$ per day for a certain machine is a Poisson random variable with mean $\lambda$. The daily cost of repairing these breakdowns is given by $C=3Y^2$. If $Y_1,...,Y_n$ denote the observed number of breakdowns for $n$ independently selected days, find an MVUE for $E(C)$. Use the Rao-Blackwell Theorem."

While looking over a solution manual to check my answers in a statistics textbook, I stumbled across the following work. How does one go from the second statement to the last?

$E(\frac{3}{n}\Sigma_{i=1}^nY^2_i | \frac{\Sigma_{i=1}^nY_i}{n})$

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