Question

Practice: Compute Likelihood of a Poisson Statistical Model

0/3 points (graded)

Let X1,…,Xn∼iidPoiss(λ∗) for some unknown λ∗∈(0,∞). You construct the associated statistical model (E,{Poiss(λ)}λ∈Θ) where E and Θ are defined as in the answers to the previous question.

Suppose you observe two samples X1=1,X2=2. What is L2(1,2,λ)? Express your answer in terms of λ.

L2(1,2,λ)=

Next, you observe a third sample X3=3 that follows X1=1 and X2=2. What is L3(1,2,3,λ)?

L3(1,2,3,λ)=

Suppose your data arrives in a different order: X1=2,X2=3,X3=1. What is L3(2,3,1,λ)?

L3(2,3,1,λ)=

Answer 1

(Y/1) (€ АX/2) L2(1, 2; A) Р(X — 1; 1) Р(Х — 2;B 4) =

L2(1,2: 4) — е 2 /2

L3(1, 2, 3; A) P(X1 1; A)P(X2=2; A) P(X3 3;A) (e/1!) (e2/2!) (e/3!

L3(1,2,3 A) e -316 /12

L3(2, 3, 1; ) P(X1 2: A)P(X2 =3; A) P(X3 1;A)(e /2!) ( e^8/3!) (e/1!)

3/12 L3(2, 3, 1; A) e