All MCQs

Positive covariance indicates that variables tend to move together, while negative covariance indicates opposite movement.
Its magnitude depends on the variables' measurement units.

The base R density() function computes a univariate kernel density estimate.
Its output can be plotted and its bandwidth can be adjusted.

KDE is primarily a local description of the observed sample.
Far-tail predictions are unreliable without substantive assumptions.

A suitable parametric model can be efficient, concise, and easy to extrapolate.
Its assumptions must be checked rather than accepted automatically.

Parametric estimation assumes a family such as normal or exponential.
The sample is then used to estimate a limited set of parameters.

KDE does not restrict the population to a finite-parameter distribution family.
Its shape is driven flexibly by the observations.

Small bandwidth lowers smoothing bias but increases random variability.
Large bandwidth reduces variability but may obscure real structure.

A density histogram is piecewise constant, while KDE is smooth.
Their common scaling allows them to be overlaid meaningfully.

Stable features persist under modest changes in smoothing.
Fragile peaks are more likely to reflect sampling noise or parameter choice.

Multiple peaks can indicate distinct groups or generating mechanisms.
Because KDE peaks depend on bandwidth, the pattern should be checked for stability.

A density's vertical value has units of probability per unit x.
Only integrated area over an interval yields a probability.

Rug marks reveal the locations and concentration of raw observations.
They help viewers connect a smooth estimate to the underlying sample.