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Statistics for Data Science II · End Term · 14 Sept 2025 · May 2025 term · Set 1

Question 10: Let be a discrete random variable with the probability m…

Question 10

+0.5 marksWritten answer

Let be a discrete random variable with the probability mass function

where

is an unknown parameter. Let be an estimator of from i.i.d , given as

Check whether is an unbiased estimator of , otherwise find an unbiased estimator of . Solution: Since we know that will be an unbiased estimator of if . Now,

Now, the values of and can be calculated as Now, substituting the values in equation(1), we get Hence, from equation(2) we can conclude that is an estimator of . Also, will be an unbiased estimator of . Consider the following options for the blanks.

Answer the given sub-questions. Note: Enter only the correct option number (e.g. 8) without any brackets or punctuation.

Let be a discrete random variable with the probability mass function
Let be a discrete random variable with the probability mass function
Let be a discrete random variable with the probability mass function
Let be a discrete random variable with the probability mass function
Let be a discrete random variable with the probability mass function

Enter the correct option number for .

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Question 10 of 27 in the IIT Madras BS Statistics for Data Science II (Stats 2) End Term paper sat on 14 Sept 2025, in the May 2025 term (Statistics2 14 Sep 25 (Session 2)). It carries 0.5 marks.

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