Practice Library
All MCQs
Browse exam-wise, subject-wise, and country-wise MCQs with explanations.
Choose an option to check your answer.
A.
Its area is normalized, so curves from different sample sizes can look similar
B.
It contains no data values
C.
It always uses one observation
D.
It replaces observations with category names
Show Answer
Correct Answer: A. Its area is normalized, so curves from different sample sizes can look similar
Explanation:
A density describes relative distribution shape rather than total count.
Choose an option to check your answer.
A.
A dendrogram kernel only
B.
A categorical bar kernel
C.
A survival censoring kernel
D.
A Gaussian kernel
Show Answer
Correct Answer: D. A Gaussian kernel
Explanation:
Gaussian kernels are popular because they are smooth and mathematically convenient.
Choose an option to check your answer.
A.
A separate probability mass that must equal one
B.
A regression line through all points
C.
A kernel function centered at the observation
D.
A category label with no numeric position
Show Answer
Correct Answer: C. A kernel function centered at the observation
Explanation:
KDE forms the estimate by averaging kernels centered at the sample values.
Choose an option to check your answer.
A.
Increase all values by an arbitrary large constant
B.
Transform the data or use a boundary-corrected estimator
C.
Delete observations near zero
D.
Use a pie chart instead
Show Answer
Correct Answer: B. Transform the data or use a boundary-corrected estimator
Explanation:
Log transformation moves a positive boundary to an unbounded scale, while specialized kernels correct leakage.
Choose an option to check your answer.
A.
Density can be incorrectly spread beyond a variable's natural boundary
B.
The plot legend covers the axis
C.
The mean lies at the chart edge
D.
The sample contains exactly two values
Show Answer
Correct Answer: A. Density can be incorrectly spread beyond a variable's natural boundary
Explanation:
Standard symmetric kernels place mass on both sides of an observation.
Choose an option to check your answer.
A.
Bandwidth changes group sample sizes
B.
Bandwidth determines category names
C.
All groups must have equal means
D.
Different smoothing levels can create artificial differences in shape
Show Answer
Correct Answer: D. Different smoothing levels can create artificial differences in shape
Explanation:
A smoother curve may look simpler merely because of its bandwidth.
Choose an option to check your answer.
A.
Every observation becomes a separate peak
B.
The density becomes a PMF
C.
Important distribution features may be oversmoothed
D.
Negative probabilities are guaranteed
Show Answer
Correct Answer: C. Important distribution features may be oversmoothed
Explanation:
Too much smoothing can merge distinct modes and hide local structure.
Choose an option to check your answer.
A.
An overly flat density
B.
A noisy density with many spurious peaks
C.
A perfectly normal curve
D.
A density with total area zero
Show Answer
Correct Answer: B. A noisy density with many spurious peaks
Explanation:
Too little smoothing follows random sample fluctuations closely.
Choose an option to check your answer.
A.
It controls the amount of smoothing
B.
It sets the sample mean
C.
It determines the number of variables
D.
It labels missing values
Show Answer
Correct Answer: A. It controls the amount of smoothing
Explanation:
Bandwidth determines how widely each observation's kernel is spread.
Choose an option to check your answer.
A.
A method that assumes every dataset is normal
B.
A discrete category-count table
C.
A clustering algorithm that requires labels
D.
A nonparametric method for estimating a smooth probability density
Show Answer
Correct Answer: D. A nonparametric method for estimating a smooth probability density
Explanation:
KDE places a smooth kernel around observations and adds their contributions.
Choose an option to check your answer.
A.
No, density values are probabilities
B.
Only for discrete variables
C.
Yes, if the total area under the curve still equals 1
D.
Only when the sample size is one
Show Answer
Correct Answer: C. Yes, if the total area under the curve still equals 1
Explanation:
Density is probability per unit of measurement, not probability itself.
Choose an option to check your answer.
A.
By adding the endpoint values only
B.
By calculating the area under the density between a and b
C.
By multiplying the mean by the variance
D.
By counting category labels
Show Answer
Correct Answer: B. By calculating the area under the density between a and b
Explanation:
For a continuous variable, interval probability equals an integral of the density.
