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Statistics for Economics Question on Mathematical statistics

Let the probability density function of the continuous random variable š‘‹ be
š‘“š‘‹š‘„, šœ† = { šœ†š‘’ āˆ’šœ†š‘„ , 0,, 0, š‘„ ā‰„ 0 otherwise ,
where šœ† > 0 is a parameter. If the observed sample values of š‘‹ are
š‘„1 = 1.75, š‘„2 = 2.25, š‘„3 = 2.50, š‘„4 = 2.75, š‘„5 = 3.25, then the Maximum Likelihood Estimator of šœ† is

A

52\frac{5}{2}

B

15\frac{1}{5}

C

15\frac{1}{5}

D

25\frac{2}{5}

Answer

25\frac{2}{5}

Explanation

Solution

The correct option is (D): 25\frac{2}{5}