Question

A continuous random variable X has a uniform distribution on the interval [5, 12]. Sketch the graph of its density function.

A) The graph is a horizontal line between 5 and 12.
B) The graph is a straight line with a slope between 5 and 12.
C) The graph is a parabolic curve between 5 and 12.
D) The graph is a vertical line between 5 and 12.

Answer 1

The correct graph of the density function for X is a horizontal line between 5 and 12. A

Characteristics of uniform distribution

A uniform distribution is characterized by a constant probability density function (PDF) over a specified interval. In this case, the random variable X has a uniform distribution on the interval [5, 12].

That means the probability of X taking any value between 5 and 12 is the same, and the density function is constant within this interval.

To sketch the graph of the density function, we would draw a horizontal line at a constant height between the x-values 5 and 12.

The height of the line represents the probability density.

Therefore, the correct graph of the density function for X is a horizontal line between 5 and 12.