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27. Test for two population proportions

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Let {X1, X2,...XN} be a random sample where each random variable X, has a PDF given by

f(x)=\frac{1}{(\lambda+\mu)} e^{\frac{1}{2}[-(\operatorname{sign}(x)+1)(x / \lambda)+(\operatorname{sign}(x)-1)(x / \mu)]}

\operatorname{sign}(x)=\left\{\begin{array}{rr}
1, & x \geq 0 \\
-1, & x<0
\end{array}\right.

where the sign function is defined as

and N denoting an integer, and the parameters , µ satisfying 1 > 0, µ > 0.In the followings provide complete derivations and explanations of results.

a) Find the likelihood function and the log-likelihood function for the parameters 1,µ

b) Find Maximum Likelihood (ML) estimators for the parameters 1, u.

c) Determine if these ML estimators are unbiased for N = 1.

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09.9.8-7-6 5 4-3

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**Use of solution provided by us for unfair practice like cheating will result in action from our end which may include permanent termination of the defaulter’s account.Disclaimer:The website contains certain images which are not owned by the company/ website. Such images are used for indicative purposes only and is a third-party content. All credits go to its rightful owner including its copyright owner. It is also clarified that the use of any photograph on the website including the use of any photograph of any educational institute/ university is not intended to suggest any association, relationship, or sponsorship whatsoever between the company and the said educational institute/ university. Any such use is for representative purposes only and all intellectual property rights belong to the respective owners.

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