SOLVED STA631 Assignment 1 Solution and Discussion

Assignment No.1 (Course STA 631)
Fall 2019 (Total Marks 20)Deadline
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The assignment is being uploaded to build up the concepts of Inferential statistics.
Assignment # 01 (Lessons 19)
Question 1: Marks: 10
Suppose are iid with pdf zero elsewhere. Find the MLE of
Question 2: Marks: 10
Let X be a Bernoulli . Thus the pdf of Bernoulli distribution is
Find the Fisher Information 
Q.1 Solution:
Q.2 Solution:

Q.1 Solution:
Q.2 Solution:

@zareen said in STA631 Assignment 1 Solution and Discussion:
Suppose are iid with pdf zero elsewhere. Find the MLE of
@zareen
3. (6.1.9) SupposeX1,…,Xnare iid with pdff(x;θ) = (1/θ)e−x/θ. Findthe mle ofP(X≤2).Answer:For this distribution we have that(θ) =−nlog(θ)−∑Xi/θ
′(θ) =−nθ+∑Xiθ2.Solving`′(θ) = 0, we see thatˆθ= ̄X.SinceP(X≤2) =∫20(1/θ)e−x/θ= 1−e−2/θ.Thus the mle ofP(X≤2) is1−e−2/ ̄X. 
@zareen said in STA631 Assignment 1 Solution and Discussion:
Let X be a Bernoulli . Thus the pdf of Bernoulli distribution is

@zareen said in STA631 Assignment 1 Solution and Discussion:
Suppose are iid with pdf zero elsewhere. Find the MLE of