Question 1
Consider an Accept-Reject method to draw samples from Beta(3, 4) distribution. Which among the following can act as a proposal distribution? Select all that apply:
Normal(0, 4)
Uniform(0, 1/2)
Bernoulli{0, 1}
F(2, 2)
Beta(0.5, 0.5)
Statistical Computing Quiz 1: 16 July 2023 (May 2023 term)
The IIT Madras BS Statistical Computing (Statistical Computing) Quiz 1 paper sat on 16 Jul 2023, in the May 2023 term: 12 questions for 35 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.
- 12
- 35
- 120 min
- 2
- 7
- 3
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Correct answers
Normal(0, 4)
F(2, 2)
Beta(0.5, 0.5)
Question 2
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Correct answers
Question 3
The method need not produce samples from F.
On average, the method will generate the samples fast.
On average, the method will generate the samples low.
There will not be any effect on the sample generation.
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Correct answer
The method need not produce samples from F.
Question 4
The mixed congruential method is used to generate pseudorandom draw of size 1000 from U(0, 1). The histogram for the 1000 generated pseudorandom numbers is as follows:
By visualizing the plotted histogram, do the pseudorandom draws appear to be i.i.d U(0, 1) distributed?
Yes
No
Insufficient information
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Correct answer
Insufficient information
Question 5
Box-Muller
Accept reject with exponential(1) proposal
Inverse transform
All of these
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Correct answer
Box-Muller
Question 6
To generate pseudorandom draws using the multiplicative congruential method, we have set seed = 5, a = 7 and m = 4. After how many steps, will the deterministic sequence follows?
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Correct answer: 2
Question 7
Use the following information and answer the given subquestions.
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Correct answer: 0.10
Question 8
Use the following information and answer the given subquestions.
An analyst advised to change the proposal distribution to Beta(2, 1). Shall we act upon his/her advice?
Yes, because it will increase the efficiency.
No, because it will reduce the efficiency.
Insufficient information to determine.
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Correct answer
No, because it will reduce the efficiency.
Question 9
Use the following information and answer the given subquestions.
Select the correct statements from the following:
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Correct answer
Question 10
Use the following information and answer the given subquestions.
Find the probability of acceptance for the accept-reject if α = 3. Enter the answer correct to three decimal places.
Note: e = 2.723
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Correct answer: 0.314 (accepted within ±0.004)
Question 11
Use the following information and answer the given subquestions.
Complete the function (1), in the given code snippet.
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Correct answer
Question 12
Use the following information and answer the given subquestions.
Which of the following is/are true about the given code snippet?
Both Inverse Transform and Accept-Reject algorithms are implemented.
Only one of Inverse Transform and Accept-Reject algorithms are implemented.
The given implemented Accept-Reject is correct as the support of function g is the same as that of function f.
The given implemented Accept-Reject is incorrect for the given function f and g.
The given implemented Inverse Transform algorithm is correct as the cumulative distribution function of f is invertible.
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Correct answer
Both Inverse Transform and Accept-Reject algorithms are implemented.