Question

A random variable X follows the exponential distribution if it has the following probability density function (pdf): f(x). The exponential distribution is commonly used to model:

a) Uniform events
b) Continuous events with a constant rate
c) Discrete events with varying rates
d) Step functions

Answer 1

The exponential distribution is commonly used to model continuous events with a constant rate.

Step-by-step explanation:

The exponential distribution is commonly used to model continuous events with a constant rate. It is often concerned with the amount of time until a specific event occurs.

An exponential random variable, X, follows the exponential distribution and has a probability density function (pdf) f(x) = me-mx, where x ≥ 0 and m > 0.

For example, the length of time between emergency arrivals at a hospital can be modeled using the exponential distribution.