Question

Explain why this is a legitimate density curve.

Short answer

Since, the curve is above the horizontal axis and the total area under the curve is $1$, we have a legitimate density curve.

Step-by-step solution

Step 1. Given

Step 2. Concept

A curve is based on a density curve.

Step 3. Explanation

A density curve has the same area underneath it as the horizontal axis and is always on or above it. A density curve depicts the overall pattern of distribution. The proportion of all observations that fall within an interval of values on the horizontal axis is represented by the area under the curve and above that interval. As a result, we obtain a valid density curve.