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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.
Very large observations are comparatively more probable
B.
All observations cluster tightly around the mean
C.
The variable becomes symmetric
D.
The support includes only negative values
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Correct Answer: A. Very large observations are comparatively more probable
Explanation:
A heavy tail decreases slowly, leaving more probability for extreme values.
Choose an option to check your answer.
A.
The symmetric uniform distribution
B.
The Bernoulli distribution only
C.
The standard normal distribution
D.
The Pareto distribution
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Correct Answer: D. The Pareto distribution
Explanation:
Pareto models describe positive values with a slowly decaying right tail.
Choose an option to check your answer.
A.
It becomes a discrete PMF
B.
It becomes uniform
C.
It becomes normally distributed under the model
D.
It loses all variation
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Correct Answer: C. It becomes normally distributed under the model
Explanation:
The defining property of a lognormal variable is normality after logging.
Choose an option to check your answer.
A.
A fair coin outcome coded as heads or tails
B.
A positive variable produced by multiplying many independent factors
C.
A fixed constant with no variation
D.
A signed error symmetric around zero
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Correct Answer: B. A positive variable produced by multiplying many independent factors
Explanation:
Multiplicative effects become additive on the logarithmic scale.
Choose an option to check your answer.
A.
Positive and right-skewed
B.
Symmetric with negative and positive support
C.
Uniform over all real values
D.
A discrete two-point distribution
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Correct Answer: A. Positive and right-skewed
Explanation:
Exponentiating a normal variable produces only positive values.
Choose an option to check your answer.
A.
When it contains only logarithm values
B.
When it is symmetric around zero
C.
When its probability mass is equal everywhere
D.
When its logarithm follows a normal distribution
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Correct Answer: D. When its logarithm follows a normal distribution
Explanation:
A lognormal variable is positive and becomes normal after taking logs.
Choose an option to check your answer.
A.
It increases the expected waiting time
B.
It makes waiting time negative
C.
It decreases the expected waiting time
D.
It leaves the distribution unchanged
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Correct Answer: C. It decreases the expected waiting time
Explanation:
For an exponential model, the mean waiting time is the reciprocal of the rate.
Choose an option to check your answer.
A.
Every event occurs at the same fixed time
B.
Remaining waiting time does not depend on how long one has already waited
C.
Past observations determine future values exactly
D.
Its mean always equals zero
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Correct Answer: B. Remaining waiting time does not depend on how long one has already waited
Explanation:
Conditional on survival to the present, the future waiting distribution is unchanged.
Choose an option to check your answer.
A.
Nonnegative real values
B.
All negative real values only
C.
Integers from 1 to 6
D.
Values strictly between -1 and 1
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Correct Answer: A. Nonnegative real values
Explanation:
Waiting times cannot be negative, so the exponential distribution begins at zero.
Choose an option to check your answer.
A.
A symmetric measurement error around zero
B.
The number of categories in a survey
C.
A variable bounded equally around its mean
D.
Waiting time until the next event in a constant-rate process
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Correct Answer: D. Waiting time until the next event in a constant-rate process
Explanation:
The exponential model describes positive waiting times between Poisson-process events.
Choose an option to check your answer.
A.
Mean 1 and variance 0
B.
Median 0 and no variance
C.
Mean 0 and standard deviation 1
D.
Mean equal to its sample size
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Correct Answer: C. Mean 0 and standard deviation 1
Explanation:
Standardization converts a normal variable to zero mean and unit standard deviation.
Choose an option to check your answer.
A.
About 25%
B.
About 68%
C.
About 50%
D.
About 99.9%
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Correct Answer: B. About 68%
Explanation:
The empirical 68-95-99.7 rule summarizes normal coverage.
