6. (18 pts) Let X be a Poisson random variable with parameter λ, and Y be an independent Poisson random variable with parameter 32. Define the estimator Y λ = ax + (1 − a)₁ - a) (8 pts) Show that  is unbiased. with 0 < a <1 3 b) (10 pts) Find the value of a which minimizes the variance of Â.

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