Question

Exercise 2. Let X1, . . . , Xn be a sample from the distribution whose density function is f(x) = 12e−|x−θ|, x ∈ R. Determine the maximum likelihood estimator of θ. [Hint: the usual method of differentiating does not work. Once you find the log-likelihood, you must carefully minimize the sum that appears there.

Name: exercise 2 let x1 xn be a sample from the distribution whose density function is fx 12ex x r determine the maximum likelihood estimator of hint the usual method of differentiating does not work once y
Uploaded: 2022-11-09T18:31:06-08:00
Duration: 4 min 1 s
Channel: David Nguyen
Description: exercise 2 let x1 xn be a sample from the distribution whose density function is fx 12ex x r determine the maximum likelihood estimator of hint the usual method of differentiating does not work once y

          Exercise 2.
Let X1, . . . , Xn be a sample from the distribution whose density function is f(x) = 12e−|x−θ|, x ∈ R.
Determine the maximum likelihood estimator of θ.
[Hint: the usual method of differentiating does not work. Once you find the log-likelihood, you must carefully minimize the sum that appears there.

Added by Kacy L.

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Solved by Expert David Nguyen

11/09/2022

Step 1

Step 1:** Calculate the likelihood function: \[ L(\theta) = \prod_{i=1}^{n} f(x_i) = \prod_{i=1}^{n} 12e^{-|x_i - \theta|} \] ** Show more…

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Exercise 2. Let X1, . . . , Xn be a sample from the distribution whose density function is f(x) = 12e−|x−θ|, x ∈ R. Determine the maximum likelihood estimator of θ. [Hint: the usual method of differentiating does not work. Once you find the log-likelihood, you must carefully minimize the sum that appears there.