Statistics for Data Science II Quiz 2: 1 December 2024 (September 2024 term)
The IIT Madras BS Statistics for Data Science II (Stats 2) Quiz 2 paper sat on 1 Dec 2024, in the September 2024 term: 17 questions for 40 marks in 120 minutes. Every question is below with its answer. Take it as a timed mock test to be marked, or read it through first.
- 17
- 40
- 120 min
- 6
- 10
- 1
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Correct answer
Question 2
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Question 3
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Correct answer: 7 (accepted within ±0.1)
Question 4
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Correct answer: 100
Question 5
Suppose a four sided fair die is thrown twice independently. Let a random variable X denote the number obtained on the first roll and a random variable Y denote the number obtained on the second roll. Define Z =| 5 − X − Y |, where | . | denotes the absolute value.
Based on the above data, answer the given subquestions.
Find the range of Z.
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Question 6
Suppose a four sided fair die is thrown twice independently. Let a random variable X denote the number obtained on the first roll and a random variable Y denote the number obtained on the second roll. Define Z =| 5 − X − Y |, where | . | denotes the absolute value.
Based on the above data, answer the given subquestions.
Find the value of P (Z = 3).
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Correct answer
Question 7
Based on the above data, answer the given subquestions.
Find the value of a. Enter the answer correct to one decimal place.
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Correct answer: 1.2 (accepted within ±0.03)
Question 8
Based on the above data, answer the given subquestions.
If E [X] = 0.7, then find the value of Var(X). Enter the answer correct to two decimal places.
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Correct answer: 0.05 (accepted within ±0.03)
Question 9
The service time at a call center follows an exponential distribution with a mean of 10 minutes. A random sample of 100 customers is selected.
Based on the above data, answer the given subquestions.
Let a random variable X represent the total service time for 100 customers. Which of the following options is an acceptable approximate model for X as per the Central Limit Theorem?
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Question 10
The service time at a call center follows an exponential distribution with a mean of 10 minutes. A random sample of 100 customers is selected.
Based on the above data, answer the given subquestions.
Using the Central Limit Theorem, find an approximate probability that the total service time for 100 customers exceeds 1200 minutes. Enter the answer correct to two decimal places.
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Correct answer: 0.025 (accepted within ±0.025)
Question 11
Based on the above data, answer the given subquestions.
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Correct answer: 12
Question 12
Based on the above data, answer the given subquestions.
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Correct answer: 0.25 (accepted within ±0.03)
Question 13
Based on the above data, answer the given subquestions.
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Question 14
Based on the above data, answer the given subquestions.
Find P (X + Y < 2). Enter the answer correct to one decimal place.
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Correct answer: 0.5
Question 15
Based on the above data, answer the given subquestions.
What is the value of a? Enter the answer correct to two decimal places.
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Correct answer: 0.06 (accepted within ±0.03)
Question 16
Based on the above data, answer the given subquestions.
If Cov (X, Y) = 0, then find the value of E [XY].
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Correct answer: 1
Question 17
Based on the above data, answer the given subquestions.
Which of the following options is/are correct?
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Correct answers