IITM BS Question 12 - Week 7 Practice

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IITM BS Question 12 - Week 7 Practice | Prasnya

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Q12Comprehension4 Marks13 Apr 2025

Passage

Based on the above data, answer the given subquestions. A service center monitors the waiting time X (in minutes) for customers, and X follows a continuous probability distribution with the probability density function (PDF):

f_X(x) = \begin{cases} \frac{3}{\theta^3} x^2, & 0 < x < \theta \\ 0, & \text{otherwise} \end{cases} where

\theta > 1$ is an unknown parameter representing the maximum possible waiting time for any customer. For a random sample of five customers, the waiting times (in minutes) are 2, 4, 1, 3, 5.

Find the method of moments estimate of

\theta

for the given sample.

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Q12

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13 Apr 2025

Statistics 2 · Week 7

Q12.Find the method of moments estimate of

\theta

for the given sample.@passage

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