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ma3014_2026T1_Q1_NA.pdf

Statistical Computing · Quiz 1 · Jan 2026

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Question 2 MCQ · 0.0 marks

[[IMAGE:1d06f69c9373e014_3_2]] [[IMAGE:1d06f69c9373e014_4_3]]
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  1. Useful Data has been mentioned above.
  2. This data attachment is just for a reference & not for an evaluation.

A published solution is not available for this question yet.

Question 3 MSQ · 2.0 marks

Which of the following statements are true about the inverse transform method? Select all that apply.
  1. It requires the inverse CDF of the distribution.
  2. It can be used only for continuous distribution.
  3. It maps a Uniform [[IMAGE:1d06f69c9373e014_4_4]] variable to the target distribution.
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  4. None of these.

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Question 4 MSQ · 2.0 marks

Suppose we want to generate samples from a discrete distribution with pmf [[IMAGE:1d06f69c9373e014_4_5]] using the Accept–Reject method. Two proposal distributions [[IMAGE:1d06f69c9373e014_5_6]] and [[IMAGE:1d06f69c9373e014_5_7]] lead to AR bounds [[IMAGE:1d06f69c9373e014_5_8]] and [[IMAGE:1d06f69c9373e014_5_9]] respectively, such that [[IMAGE:1d06f69c9373e014_5_10]] . Which of the following statements are true? Select all that apply.
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  1. Both proposals generate samples from [[IMAGE:1d06f69c9373e014_5_11]] with the same efficiency.
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  2. We cannot comment on the efficiency based on the AR bounds.
  3. [[IMAGE:1d06f69c9373e014_5_12]] will produce faster samples from [[IMAGE:1d06f69c9373e014_5_13]] .
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  4. Both proposals have the same acceptance probability.

A published solution is not available for this question yet.

Question 5 MCQ · 4.0 marks

Consider the following two multiplicative congruential generators with seed [[IMAGE:1d06f69c9373e014_5_14]] as [[IMAGE:1d06f69c9373e014_5_15]] [[IMAGE:1d06f69c9373e014_5_16]] Starting from the given seed, which of the following statements is correct?
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  1. The sequence generated by [[IMAGE:1d06f69c9373e014_5_17]] starts repeating before the sequence generated by [[IMAGE:1d06f69c9373e014_5_18]] .
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  2. The sequence generated by [[IMAGE:1d06f69c9373e014_5_19]] starts repeating before the sequence generated by [[IMAGE:1d06f69c9373e014_5_20]] .
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  3. Both sequences start repeating at the same step.
  4. No repetition for [[IMAGE:1d06f69c9373e014_5_21]] and [[IMAGE:1d06f69c9373e014_5_22]] .
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A published solution is not available for this question yet.

Question 6 MCQ · 4.0 marks

Suppose [[IMAGE:1d06f69c9373e014_6_23]] with probability density function [[IMAGE:1d06f69c9373e014_6_24]] We wish to generate random samples from this distribution using the Ratio of Uniforms (RoU) method. The RoU set is defined as [[IMAGE:1d06f69c9373e014_6_25]] Suppose you enclose the set [[IMAGE:1d06f69c9373e014_6_26]] in a box [[IMAGE:1d06f69c9373e014_6_27]] for the accept-reject step. Find the values of [[IMAGE:1d06f69c9373e014_6_28]] , [[IMAGE:1d06f69c9373e014_6_29]] , and [[IMAGE:1d06f69c9373e014_6_30]] .
Source diagram or notationSource diagram or notationSource diagram or notationSource diagram or notationSource diagram or notationSource diagram or notationSource diagram or notationSource diagram or notation
  1. [[IMAGE:1d06f69c9373e014_6_31]]
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  2. [[IMAGE:1d06f69c9373e014_6_32]]
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  3. [[IMAGE:1d06f69c9373e014_6_33]]
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  4. [[IMAGE:1d06f69c9373e014_6_34]]
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A published solution is not available for this question yet.

Question 7 MCQ · 3.0 marks

Let a random variable [[IMAGE:1d06f69c9373e014_6_35]] have the following probability mass function : [[IMAGE:1d06f69c9373e014_6_36]] Let [[IMAGE:1d06f69c9373e014_6_37]] . Which of the following correctly constructs [[IMAGE:1d06f69c9373e014_6_38]] with distribution function [[IMAGE:1d06f69c9373e014_6_39]] using the inverse transform method?
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  1. [[IMAGE:1d06f69c9373e014_6_40]]
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  2. [[IMAGE:1d06f69c9373e014_7_41]]
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  3. [[IMAGE:1d06f69c9373e014_7_42]]
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  4. [[IMAGE:1d06f69c9373e014_7_43]]
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A published solution is not available for this question yet.

Question 8 MCQ · 2.0 marks

Below code snippet implements an inverse transform method. Study the code carefully and answer the given subquestions. [[IMAGE:1d06f69c9373e014_7_44]] [[IMAGE:1d06f69c9373e014_8_45]] [[IMAGE:1d06f69c9373e014_8_46]]
What is the CDF of the [[IMAGE:1d06f69c9373e014_8_47]]
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  1. [[IMAGE:1d06f69c9373e014_8_48]]
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  2. [[IMAGE:1d06f69c9373e014_9_49]]
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  3. [[IMAGE:1d06f69c9373e014_9_50]]
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  4. [[IMAGE:1d06f69c9373e014_9_51]]
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A published solution is not available for this question yet.

Question 9 MSQ · 2.0 marks

Below code snippet implements an inverse transform method. Study the code carefully and answer the given subquestions. [[IMAGE:1d06f69c9373e014_7_44]] [[IMAGE:1d06f69c9373e014_8_45]] [[IMAGE:1d06f69c9373e014_8_46]]
Based on the inverse CDF plot and the histogram of generated samples, select all correct statements.
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  1. The density of [[IMAGE:1d06f69c9373e014_9_52]] increases as [[IMAGE:1d06f69c9373e014_9_53]] increases.
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  2. The inverse CDF plot indicates that values near 0 on the horizontal axis produce small values of [[IMAGE:1d06f69c9373e014_9_54]] .
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  3. The distribution of [[IMAGE:1d06f69c9373e014_9_55]] is left skewed.
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  4. The distribution of [[IMAGE:1d06f69c9373e014_9_56]] is right skewed.
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A published solution is not available for this question yet.

Question 10 NAT · 2.0 marks

Below code snippet implements an inverse transform method. Study the code carefully and answer the given subquestions. [[IMAGE:1d06f69c9373e014_7_44]] [[IMAGE:1d06f69c9373e014_8_45]] [[IMAGE:1d06f69c9373e014_8_46]]
If [[IMAGE:1d06f69c9373e014_9_57]] , then compute the value of [[IMAGE:1d06f69c9373e014_9_58]] . Enter the answer correct to one decimal place.
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    A published solution is not available for this question yet.

    Question 11 MCQ · 3.0 marks

    Suppose that we want to simulate a discrete random variable [[IMAGE:1d06f69c9373e014_10_59]] using a mixture of two discrete random variables [[IMAGE:1d06f69c9373e014_10_60]] and [[IMAGE:1d06f69c9373e014_10_61]] . Consider the simulation procedure as follows: [[IMAGE:1d06f69c9373e014_10_62]] The probability mass functions of [[IMAGE:1d06f69c9373e014_10_63]] and [[IMAGE:1d06f69c9373e014_10_64]] are given by: [[IMAGE:1d06f69c9373e014_10_65]] and [[IMAGE:1d06f69c9373e014_10_66]] Based on the above data, answer the given subquestions.
    Identify the correct PMF of [[IMAGE:1d06f69c9373e014_10_67]] in terms of [[IMAGE:1d06f69c9373e014_10_68]] and [[IMAGE:1d06f69c9373e014_10_69]] .
    Source diagram or notationSource diagram or notationSource diagram or notationSource diagram or notationSource diagram or notationSource diagram or notationSource diagram or notationSource diagram or notationSource diagram or notationSource diagram or notationSource diagram or notation
    1. [[IMAGE:1d06f69c9373e014_10_70]]
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    2. [[IMAGE:1d06f69c9373e014_10_71]]
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    3. [[IMAGE:1d06f69c9373e014_10_72]]
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    4. [[IMAGE:1d06f69c9373e014_11_73]]
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    A published solution is not available for this question yet.

    Question 12 NAT · 2.0 marks

    Suppose that we want to simulate a discrete random variable [[IMAGE:1d06f69c9373e014_10_59]] using a mixture of two discrete random variables [[IMAGE:1d06f69c9373e014_10_60]] and [[IMAGE:1d06f69c9373e014_10_61]] . Consider the simulation procedure as follows: [[IMAGE:1d06f69c9373e014_10_62]] The probability mass functions of [[IMAGE:1d06f69c9373e014_10_63]] and [[IMAGE:1d06f69c9373e014_10_64]] are given by: [[IMAGE:1d06f69c9373e014_10_65]] and [[IMAGE:1d06f69c9373e014_10_66]] Based on the above data, answer the given subquestions.
    Find the value of [[IMAGE:1d06f69c9373e014_11_74]] . Enter the answer correct to two decimal places.
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      A published solution is not available for this question yet.

      Question 13 MCQ · 1.0 marks

      Suppose that we want to simulate a discrete random variable [[IMAGE:1d06f69c9373e014_10_59]] using a mixture of two discrete random variables [[IMAGE:1d06f69c9373e014_10_60]] and [[IMAGE:1d06f69c9373e014_10_61]] . Consider the simulation procedure as follows: [[IMAGE:1d06f69c9373e014_10_62]] The probability mass functions of [[IMAGE:1d06f69c9373e014_10_63]] and [[IMAGE:1d06f69c9373e014_10_64]] are given by: [[IMAGE:1d06f69c9373e014_10_65]] and [[IMAGE:1d06f69c9373e014_10_66]] Based on the above data, answer the given subquestions.
      Can we say [[IMAGE:1d06f69c9373e014_11_75]]
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      1. Yes
      2. No

      A published solution is not available for this question yet.

      Question 14 NAT · 3.0 marks

      Suppose we want to obtain samples from a distribution with pdf [[IMAGE:1d06f69c9373e014_11_76]] by using the accept-reject method. Find the probability of acceptance for [[IMAGE:1d06f69c9373e014_11_77]] as a proposal distribution. Enter the answer correct to two decimal places.
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        A published solution is not available for this question yet.