Quiz Space

Statistics for Data Science II · End Term · 13 Apr 2025 · January 2025 term · Set QDF1

Question 9: Find the maximum likelihood estimate of λ for the given s…

Question 9

+3 marksNumerical answer

A research team is analyzing customer complaints per day for a new service. The number of complaints X follows a Poisson distribution with an unknown average rate λ. The number of complaints observed over a period of 10 days are as follows :
3, 5, 2, 4, 6, 3, 4, 7, 5, 4
The team aims to estimate λ using two different methods: Maximum Likelihood Estimation (MLE) and Bayesian Estimation.
Based on the above data, answer the given subquestions.

Find the maximum likelihood estimate of λ for the given sample. Enter the answer correct to one decimal place.

Show answer

Correct answer: 4.3 (accepted within ±0.2)

See the whole paperTake it as a mock test

Question 9 of 17 in the IIT Madras BS Statistics for Data Science II (Stats 2) End Term paper sat on 13 Apr 2025, in the January 2025 term (IIT M FOUNDATION FN EXAM QDF1 13 Apr 2025). It carries 3 marks.

More questions from this paper

  1. Q1Figure question
  2. Q2Figure question
  3. Q3Figure question
  4. Q4Figure question
  5. Q5The company assumes a Beta(1.4, b) prior for p. Given that prior knowledge suggests the expected value of p is approxim…
  6. Q6Using the prior distribution and the observed data, compute the posterior distribution of p.
  7. Q7Find the method of moments estimate of θ for the given sample.
  8. Q8The company has a policy requirement that the average waiting time must not exceed 3 minutes. Based on the estimated va…
  9. Q10Assume the prior distribution of λ to be Gamma(3, 2). Determine the posterior distribution of λ.
  10. Q11Based on the above data, answer the given subquestions.
  11. Q12Based on the above data, answer the given subquestions.
  12. Q13Based on the above data, answer the given subquestions.
  13. Q14Based on the above data, answer the given subquestions.
  14. Q15Based on the above data, answer the given subquestions.
  15. Q16Based on the above data, answer the given subquestions.
  16. Q17Based on the above data, answer the given subquestions.