ma3014_2023T2_Q1_NA.pdf

Statistical Computing · Quiz 1 · May 2023

Questions and published explanations below are available without starting a test. Some questions may not have a published solution yet.

Question 157 MSQ · 3.0 marks

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)

A published solution is not available for this question yet.

Question 158 MSQ · 3.0 marks

[[IMAGE:e8a4a4186555bf13_3_1]]

[[IMAGE:e8a4a4186555bf13_3_2]]
[[IMAGE:e8a4a4186555bf13_3_3]]
[[IMAGE:e8a4a4186555bf13_3_4]]
[[IMAGE:e8a4a4186555bf13_3_5]]

A published solution is not available for this question yet.

Question 159 MCQ · 2.0 marks

[[IMAGE:e8a4a4186555bf13_4_6]]

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.

A published solution is not available for this question yet.

Question 160 MCQ · 2.0 marks

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: [[IMAGE:e8a4a4186555bf13_4_7]] By visualizing the plotted histogram, do the pseudorandom draws appear to be i.i.d U(0, 1) distributed?

Yes
No
Insufficient information

A published solution is not available for this question yet.

Question 161 MCQ · 2.0 marks

[[IMAGE:e8a4a4186555bf13_5_8]]

Box-Muller
Accept reject with exponential(1) proposal
Inverse transform
All of these

A published solution is not available for this question yet.

Question 162 NAT · 3.0 marks

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?

A published solution is not available for this question yet.

Question 163 NAT · 3.0 marks

Use the following information and answer the given subquestions. [[IMAGE:e8a4a4186555bf13_6_9]]

[[IMAGE:e8a4a4186555bf13_7_10]]

A published solution is not available for this question yet.

Question 164 MCQ · 2.0 marks

Use the following information and answer the given subquestions. [[IMAGE:e8a4a4186555bf13_6_9]]

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.

A published solution is not available for this question yet.

Question 165 MCQ · 4.0 marks

Use the following information and answer the given subquestions. [[IMAGE:e8a4a4186555bf13_8_11]]

Select the correct statements from the following:

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[[IMAGE:e8a4a4186555bf13_8_13]]
[[IMAGE:e8a4a4186555bf13_8_14]]
[[IMAGE:e8a4a4186555bf13_8_15]]

A published solution is not available for this question yet.

Question 166 NAT · 3.0 marks

Use the following information and answer the given subquestions. [[IMAGE:e8a4a4186555bf13_8_11]]

Find the probability of acceptance for the accept-reject if α = 3. Enter the answer correct to three decimal places. Note: e = 2.723

A published solution is not available for this question yet.

Question 167 MCQ · 4.0 marks

Use the following information and answer the given subquestions. [[IMAGE:e8a4a4186555bf13_10_16]]

Complete the function (1), in the given code snippet.

[[IMAGE:e8a4a4186555bf13_10_17]]
[[IMAGE:e8a4a4186555bf13_10_18]]
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[[IMAGE:e8a4a4186555bf13_11_20]] [[IMAGE:e8a4a4186555bf13_11_21]]
[[IMAGE:e8a4a4186555bf13_11_22]]

A published solution is not available for this question yet.

Question 168 MCQ · 4.0 marks

Use the following information and answer the given subquestions. [[IMAGE:e8a4a4186555bf13_10_16]]

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. **Advanced Algorithms** **Section Id :** 64065339133 **Section Number :** 9 **Section type :** Online **Mandatory or Optional :** Mandatory **Number of Questions :** 12

A published solution is not available for this question yet.