Question

1. Properties of the uniform, normal, and exponential distributions Aa Aa Suppose that x1 is a uniformly distributed random variable, x2 is a normally distributed random variable, and x3 is an exponentially distributed random variable. For each of the following statements, indicate whether it applies to x1, x2, and/or x3. Check all that apply. x2 x3 (uniform) (normal) (exponential) The area under the graph of the probability density function to the right of the mean equals 0.5. Probabilities are given by areas under the graph of the probability density function f(x) x is the uncertain time or space interval between consecutive events in a Poisson process.

Answer 1

This is true for all three distributions. Mean is the point where the area to the left of the mean equals the area to the right of the mean which equals 0.5.

Thus, this is true for uniform, normal and the exponential distributions.

This is also true for all the three distributions. This is a general property of a PDF. The area under the graph of the PDF denotes probabilities.

Thus, this is true for uniform, normal and the exponential distributions.

This is the definition of the random variable in an exponential distribution. Thus, this is true only for the exponential distribution.