Question 1
Two 4-sided fair dice are rolled. If the sum of the numbers on the two dice is less than or equal to 7, then find the conditional probability that the number on the first die is 4.
Stats 2 End Term: 30 April 2023, Set QPF1-S1 (January 2023 term)
The IIT Madras BS Statistics for Data Science II (Stats 2) End Term paper sat on 30 Apr 2023, in the January 2023 term, set QPF1-S1: 15 questions for 40 marks in 180 minutes. Every question is below with its answer. Take it as a timed mock test to be marked, or read it through first.
- 15
- 40
- 180 min
- 8
- 1
- 6
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Correct answer: 0.2 (accepted within ±0.03)
Question 2
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Correct answer: 7
Question 3
Suppose X is a random variable whose distribution has an unknown parameter θ and Y is a zero mean random variable. Which of the following must be true?
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Correct answers
Question 4
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Correct answer
Question 5
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Correct answer
Question 6
Let X be a random variable with PMF as follows:
Define another random variable Y = 2X + 3.
Based on the above data, answer the given subquestions.
What is the standard deviation of Y ?
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Correct answer: 1
Question 7
Let X be a random variable with PMF as follows:
Define another random variable Y = 2X + 3.
Based on the above data, answer the given subquestions.
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Correct answer
Question 8
Based on the above data, answer the given subquestions.
Find the value of c.
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Correct answer
Question 9
Based on the above data, answer the given subquestions.
Find the value of P(X < 1, Y < 3). Enter the answer correct to three decimal places.
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Correct answer: 0.375 (accepted within ±0.003)
Question 10
Based on the above data, answer the given subquestions.
Find the method of moments estimate of θ for the given sample. Enter the answer correct to two decimal places.
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Correct answer: 0.25 (accepted within ±0.02)
Question 11
Based on the above data, answer the given subquestions.
Find the maximum likelihood estimate of θ for the given sample. Enter the answer correct to two decimal places.
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Correct answer: 0.25 (accepted within ±0.02)
Question 12
Based on the above data, answer the given subquestions.
Find the posterior distribution of p.
Gamma(39,11)
Beta(40, 16)
Gamma(40,16)
Gamma(40,11)
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Correct answer
Gamma(40,11)
Question 13
Based on the above data, answer the given subquestions.
Find the posterior mean. Enter the answer correct to two decimal places.
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Correct answer: 3.64 (accepted within ±0.04)
Question 14
A manufacturer produces cotter pins and claims that the probability of a randomly selected cotter pin being defective is 0.3. However, an analyst suspects that the claimed probability value is too high and decides to verify it by conducting a test. The analyst randomly selects 8 cotter pins from the manufacturer’s production line and inspects them for defects. If less than 2 cotter pins are defective (out of those 8 cotter pins), then the analyst rejects the claim, or else he accepts it. Based on the above data, answer the given subquestions.
Define null hypothesis and alternative hypothesis.
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Correct answer
Question 15
A manufacturer produces cotter pins and claims that the probability of a randomly selected cotter pin being defective is 0.3. However, an analyst suspects that the claimed probability value is too high and decides to verify it by conducting a test. The analyst randomly selects 8 cotter pins from the manufacturer’s production line and inspects them for defects. If less than 2 cotter pins are defective (out of those 8 cotter pins), then the analyst rejects the claim, or else he accepts it. Based on the above data, answer the given subquestions.
Find the significance level of the test. Enter the answer correct to two decimal places.
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Correct answer: 0.26 (accepted within ±0.03)