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

Question 15: Using the posterior distribution, calculate the posterio…

Question 15

+2 marksWritten answer

A factory manufactures light bulbs, and each bulb has a probability of being defective. To estimate this probability using Bayesian methods, assume the prior distribution of to be Beta(3, 3). A quality inspector tests 12 independent bulbs. If 5 bulbs are found to be defective, answer the given subquestions.

Using the posterior distribution, calculate the posterior mean of . Enter the answer correct to two decimal places.

Show answer

A written answer, not marked automatically.

See the whole paper Take it as a mock test

Question 15 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 2 marks.

More questions from this paper

Q1Figure question
Q2A supermarket manager claims that the average billing time for customers is 12 minutes with a known standard deviation …
Q3Consider the samples {1, 3, 4, 6, 2} taken from a Poisson Distribution with an unknown parameter . Using a Gamma(5, 8) …
Q4The joint probability density function of two continuous random variables and is given as, Find the marginal density of…
Q5Let be a discrete random variable with the probability mass function where is an unknown parameter. Let be an estimator…
Q6Let be a discrete random variable with the probability mass function where is an unknown parameter. Let be an estimator…
Q7Let be a discrete random variable with the probability mass function where is an unknown parameter. Let be an estimator…
Q8Let be a discrete random variable with the probability mass function where is an unknown parameter. Let be an estimator…
Q9Let be a discrete random variable with the probability mass function where is an unknown parameter. Let be an estimator…
Q10Let be a discrete random variable with the probability mass function where is an unknown parameter. Let be an estimator…
Q11A nutrition company claims that the average protein content of its energy bars is 20 grams, with a known standard devia…
Q12Compute the sample variance of the 5 temperature readings from the new sensor. Enter the answer correct to one decimal …
Q13At significance level, determine whether the new sensor has less variability than the old sensor.
Q14Determine the posterior distribution of .
Q16The probability density function of a continuous random variable is given by Based on the above data, answer the given …
Q17The probability density function of a continuous random variable is given by Based on the above data, answer the given …
Q18The joint PMF of two discrete random variables and is given in the following table: Based on the above data, answer the…
Q19The joint PMF of two discrete random variables and is given in the following table: Based on the above data, answer the…
Q20Let the random variable represent the number of issues resolved during a customer support call. The probability mass fu…
Q21Let the random variable represent the number of issues resolved during a customer support call. The probability mass fu…
Q22Let be a discrete random variable with the probability mass function where is an unknown parameter. Let be an estimator…
Q23A laboratory is testing a new temperature sensor to check whether it provides more consistent readings than the old mod…
Q24A factory manufactures light bulbs, and each bulb has a probability of being defective. To estimate this probability us…
Q25The probability density function of a continuous random variable is given by Based on the above data, answer the given …
Q26The joint PMF of two discrete random variables and is given in the following table: Based on the above data, answer the…
Q27Let the random variable represent the number of issues resolved during a customer support call. The probability mass fu…