Question

1. which of the following cannot be a density curve? check all that apply.

Explanation:

Step1: Recall the properties of a density curve

A density curve must satisfy two conditions: 1. It is always on or above the \(x -\)axis (non - negative). 2. The total area under the curve is \(1\).

Step2: Analyze each option

• Option A: The curve is non - negative and the area under the curve can be \(1\).
• Option B: The curve is non - negative and the area under the curve can be \(1\) (for example, if it is a uniform distribution over a certain interval).
• Option C: The curve is non - negative and the area under the curve can be \(1\).
• Option D: Part of the curve is below the \(x -\)axis. Since a density curve must be non - negative (always on or above the \(x -\)axis), this cannot be a density curve.
• Option E: The curve is non - negative and the area under the curve can be \(1\).

Answer:

D.