STAT6110/STAT3110: Independent and Identically Distributed Uniform - Density Function - Statistics Assignment Help

Assignment Task:

1. Suppose that U₁, . . . , U_n are independent and identically distributed Uniform(0,1) random variables with probability density function.

(a) Show that both of the pooled estimators L₁ and L₂ are unbiased estimators of λ.
(b) Find Var(L₁) and Var(L₂).
(c) Show that both estimators are consistent estimators of λ.
(d) Derive the efficiency of the estimator L₁ relative to L₂.
(e) State which estimator is preferable and provide a reason.

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