Exercise 1 let x1 xn be a sample from the distribution whose...

Exercise 1. Let X1, . . . , Xn be a sample from the distribution whose density function is f(x) = e−(x−θ), x ≥ θ; 0 otherwise Determine the maximum likelihood estimator of θ. [Hint: one must reason similarly as to the uniform distribution]

Transcript

00:01 Hi, i'm david and i'm here to help you and see the question.

00:03 Now let me pick up your question here.

00:05 In the question here, we are given the function, the random variable x1 up to xn, has the density function here.

00:12 I'm going to determine the maximum likelihood estimator for the tita.

00:16 First of all i need to find, write down the lacquit function l theta and it's equal to the product, i agree from 1 um to the n, the f.

00:25 X i.

00:26 Equal to the product, i equal to 1 to the n.

00:30 The density will be the e to the power minus xi minus tita.

00:36 And we have two times in the indicator that the xi will be quite equal to the theta.

00:42 And now from here we will write down the lock like node function l with small l on the titor.

00:50 This is an identical to the element of the comptal of the teta.

00:54 And then when we turn the...

00:56 The land here we should get equal to the product becomes a summation i go from 1 up to the end and land of the exponential will be cancelled now that we have the minus campaign outside inside we have the xi minus the theta and then this will be the plus and this one will be a land of the indicator function of the xi greater equal to the theta and then it will try to maximize the lock like new function here.

01:30 We try to draw the graph of the lock like glue function.

01:37 So this one will be the theta and this will mean the l -teta...

Question

Exercise 1. Let X1, . . . , Xn be a sample from the distribution whose density function is f(x) = e−(x−θ), x ≥ θ; 0 otherwise Determine the maximum likelihood estimator of θ. [Hint: one must reason similarly as to the uniform distribution]

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