Question

Let θ be an unknown constant. Let W1,…,Wn be independent exponential random variables each with parameter 1. Let Xi=θ+Wi.

What is the maximum likelihood estimate of θ based on a single observation X1=x1? Enter your answer in terms of x1 (enter as x_1) using standard notation .

θ^ML(x1)= - unanswered


e−x1
What is the maximum likelihood estimate of θ based on a sequence of observations (X1,…,Xn)=(x1,…,xn)?
θ^ML(x1,…,xn)=

(x1x2⋯xn)1/n x1+⋯+xnn 11x1+⋯1xn minixi maxixi None of the above

You have been asked to construct a confidence interval of the particular form [Θ^−c,Θ^], where Θ^=mini{Xi} and c is a constant that we need to choose. For n=10, how should the constant c be chosen so that we have a 95% confidence interval? (Give the smallest possible value of c.) Your answer should be accurate to 3 decimal places.

Answer 1

display.cgi?id=1400611807

Answer 2

c = 0.098

Answer 3

Is that the right answer for c?

Answer 4

c = 0.098 wrong.
anyone got maximum likelihood estimate of è based on a sequence of observations?

Answer 5

b) min Xi

Answer 6

Might help for c:
P(minXi<a) means
1-P(minXi>a) which means
1-P(allXi>a).

Answer 7

any ideas for c?

Answer 8

a) x_1

Answer 9

c=0,414

Answer 10

true value for c = 0.29957