Due: Feb 8, 2021. 23:59 pm.
HW 1
Textbook 4.2.3 (a, b) (7th ed: 4.2.4 ab), 4.2.6, (7th ed 4.2.7), 4.2.14, 4.2.17, 4.2.18, 4.2.19, 4.2.21, 4.2.22.
1. The mean square error (MSE) of an estimator θˆ with respect to the unknown parameter θ is defined as MSE(θˆ) = E[(θˆ − θ)2].
(a) Show that if θˆ is an unbiased estimator for θ then
MSE(θˆ) = Var[θˆ]
(b) Show that in general,
2. Let X1, X2, X3 be independent Poisson random variables with means θ, 2θ, and 3θ, respectively. Let θˆ =
X1+X2+X3 . Is θˆ an unbiased estimator for θ? Explain. Also find the variance of θˆ. 6
MSE(θˆ) = Var[θˆ] + [E(θˆ − θ)]2
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