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Statistics for Data Science II · End Term · 24 Dec 2023 · September 2023 term · Set FDF1

Question 7: Let a random sample of X be 6, 7.5, 7.5, 3, 6. Find the m…

Question 7

+3 marksNumerical answer

Based on the above data, answer the given subquestions.

Let a random sample of X be 6, 7.5, 7.5, 3, 6. Find the maximum likelihood estimate of α for the given sample.

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Correct answer: 3

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Question 7 of 15 in the IIT Madras BS Statistics for Data Science II (Stats 2) End Term paper sat on 24 Dec 2023, in the September 2023 term (IIT M FOUNDATION FN EXAM FDF1 24 Dec 2023). It carries 3 marks.

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  1. Q1Figure question
  2. Q2Figure question
  3. Q3Figure question
  4. Q4Figure question
  5. Q5Figure question
  6. Q6Let a random sample of X be 1, 2, 2.5, 2.5, 2. Find the method of moments estimate of α for the given sample.
  7. Q8Which of the following option(s) is (are) true about the moment generating function of the random variable Y ?
  8. Q9Find the expected value of Y .
  9. Q10Define null hypothesis and alternative hypothesis.
  10. Q11Find the power of the test for μ = 11. Enter the answer correct to two decimal places.
  11. Q12Find the posterior distribution of p for a Uniform [0, 1] prior.
  12. Q13Find the posterior mean. Enter the answer correct to two decimal places.
  13. Q14What is the probability that a randomly selected light bulb will last more than 150 hours?
  14. Q15Find P(X > 300 | X > 200). Enter the answer correct to two decimal places.