All MCQs

Continuous probability is assigned to intervals through area.
An individual point contributes no area even when the density there is positive.

A density distributes total probability across the variable's support.
Therefore, the complete area under the curve must be one.

A model is misspecified when key assumptions about shape, dependence, or support are wrong.
Diagnostics and sensitivity analysis help reveal the problem.

Scale parameters expand or contract a distribution around its location.
Standard deviation is the normal distribution's scale parameter.

Location parameters determine where a distribution is centered.
Changing location moves the model without necessarily changing its shape.

A normal distribution has support over the entire real line.
For positive skewed data, this may assign unrealistic probability to negative outcomes.

Support, mechanisms, and plausible tail behavior depend on the real process.
A model should be both empirically adequate and scientifically sensible.

Nonlinear patterns indicate differences in skewness or tail behavior.
Random small deviations are expected, but systematic curvature is diagnostic.

A Q-Q plot pairs empirical quantiles with theoretical quantiles.
Agreement near a line supports the proposed distributional form.

A single moment does not capture skewness, modality, or extreme behavior.
Model checks should compare multiple features of the empirical distribution.

Fitting chooses parameter values that make a model compatible with the sample.
The result should then be assessed using diagnostics and context.

Power-law relationships can appear approximately linear on logarithmic axes.
Departures from linearity indicate that a pure Pareto tail may be inadequate.