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All MCQs
Browse exam-wise, subject-wise, and country-wise MCQs with explanations.
Choose an option to check your answer.
A.
They are equal
B.
The mean is always largest
C.
The median is always smallest
D.
The mode is undefined
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Correct Answer: A. They are equal
Explanation:
Symmetry and unimodality place all three measures at the center.
Choose an option to check your answer.
A.
A constant horizontal mass at discrete points
B.
A strictly decreasing step function
C.
A two-peak curve in every case
D.
A symmetric bell-shaped curve
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Correct Answer: D. A symmetric bell-shaped curve
Explanation:
The normal density is symmetric around its mean and has one central peak.
Choose an option to check your answer.
A.
The Pareto distribution without parameters
B.
Every bimodal distribution
C.
The normal distribution
D.
An arbitrary empirical distribution
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Correct Answer: C. The normal distribution
Explanation:
A normal distribution is specified by a location parameter and a scale parameter.
Choose an option to check your answer.
A.
By replacing all outcomes with their mean
B.
By using the proportion of simulated trials in which the event occurs
C.
By selecting the largest simulated value
D.
By drawing one trial only
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Correct Answer: B. By using the proportion of simulated trials in which the event occurs
Explanation:
Repeated simulated trials approximate the event's long-run frequency.
Choose an option to check your answer.
A.
Quantiles corresponding to cumulative probabilities
B.
Histogram bin counts
C.
Cluster memberships
D.
Covariance matrices
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Correct Answer: A. Quantiles corresponding to cumulative probabilities
Explanation:
A quantile function inverts the CDF.
Choose an option to check your answer.
A.
Random draws
B.
Parameter estimates
C.
Sorted observations
D.
Cumulative probabilities
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Correct Answer: D. Cumulative probabilities
Explanation:
The p-prefix evaluates the cumulative distribution function.
Choose an option to check your answer.
A.
Random samples
B.
Cumulative probabilities
C.
Density or probability mass values
D.
Quantiles
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Correct Answer: C. Density or probability mass values
Explanation:
The d-prefix evaluates a density for continuous distributions or mass for discrete ones.
Choose an option to check your answer.
A.
dunif() only
B.
runif()
C.
punif() only
D.
qunif() only
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Correct Answer: B. runif()
Explanation:
Functions beginning with r generate random variates in R's distribution naming convention.
Choose an option to check your answer.
A.
rnorm(100)
B.
runif(0, 100)
C.
pnorm(100)
D.
qnorm(100)
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Correct Answer: A. rnorm(100)
Explanation:
rnorm() generates normal random variates, and the first argument is the number requested.
Choose an option to check your answer.
A.
Every selected item is permanently removed
B.
Only missing items can be sampled
C.
The sample must equal the population size
D.
A selected item can be chosen again in the same sample
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Correct Answer: D. A selected item can be chosen again in the same sample
Explanation:
After each draw, the item is returned to the sampling pool.
Choose an option to check your answer.
A.
It eliminates Monte Carlo error
B.
It proves the model is correct
C.
It allows results and debugging steps to be repeated exactly
D.
It guarantees independent real-world observations
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Correct Answer: C. It allows results and debugging steps to be repeated exactly
Explanation:
A fixed seed lets collaborators recreate the same simulated sample.
Choose an option to check your answer.
A.
A value chosen manually without rules
B.
A deterministic sequence designed to behave like random draws
C.
A number that can never be reproduced
D.
A missing numeric observation
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Correct Answer: B. A deterministic sequence designed to behave like random draws
Explanation:
Computer generators use algorithms and an internal state to produce random-like sequences.
