Suppose that X, X..... X are i.i.d. with density function f(x|0) = e(x-8), x0 and f(x1)...

 

Transcribed Image Text:

Suppose that X₁, X₂..... X are i.i.d. with density function f(x|0) = e(x-8), x≥0 and f(x1) = 0 otherwise. a Find the method of moments estimate of 0. b Find the mle of 0. (Hint: Be careful, and don't differentiate before thinking. For what values of is the likelihood positive?) 2a. Notice that the density is that of T+0 where T has the exponential density with parameter 1. Therefore the first moment of the density is = E(T) +0=1+0, and therefore 0= ₁-1. Therefore the MOM estimate is MOMX-1. b. It is important to notice that with probability 1,0 min(X1, X2,..., Xn). So the likelihood function is -n.X Suppose that X₁, X₂..... X are i.i.d. with density function f(x|0) = e(x-8), x≥0 and f(x1) = 0 otherwise. a Find the method of moments estimate of 0. b Find the mle of 0. (Hint: Be careful, and don't differentiate before thinking. For what values of is the likelihood positive?) 2a. Notice that the density is that of T+0 where T has the exponential density with parameter 1. Therefore the first moment of the density is = E(T) +0=1+0, and therefore 0= ₁-1. Therefore the MOM estimate is MOMX-1. b. It is important to notice that with probability 1,0 min(X1, X2,..., Xn). So the likelihood function is -n.X

Answer rating: 100% (QA)

The images you have provided show a question regarding finding the method of moments estimate and the maximum likelihood estimate MLE of a parameter t... View the full answer