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

Question

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)= x_1 - correct

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

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.

c=

Answer 1

please solve this problem guys

Answer 2

anyone there who can present the solution

Answer 3

Please, help

Answer 4

display.cgi?id=1432531325

Answer 5

c = 0.098

Answer 6

c = 0.098 wrong.

Answer 7

anyone got maximum likelihood estimate of è based on a sequence of observations?

Answer 8

maximum likelihood estimator is mini{Xi}

Answer 9

Anyone got right answer for c = ?

Answer 10

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

Answer 11

any ideas for c?

Answer 12

0.414

Answer 13

The true value for c = 0.29957

Answer 14

thanks

Answer 15

thanks, but that was too late!