If the parameter of an exponential distribution is 1,then which of the following is true?
A)The density function is e−x for x ≥ 0.
B)The mean is equal to 1.
C)The standard deviation and variance are both equal to 1.
D)All of these choices are true.

Question

Quizplus · Accepted Answer

If the parameter of an exponential distribution is 1, then:
A) The density function is e^(-x) for x ≥ 0. This is true for any exponential distribution.
B) The mean can be found by dividing the parameter (in this case 1) by 1, so the mean is 1/1 = 1. Therefore, this is true.
C) The standard deviation for an exponential distribution with parameter λ is equal to 1/λ. Hence, in this case, the standard deviation is 1. The variance of an exponential distribution with parameter λ is equal to 1/λ^2. Therefore, in this case, the variance is equal to 1/1^2 = 1. Therefore, this is also true.
D) As A, B, and C are all true, the correct answer is D.

If the Parameter of an Exponential Distribution Is 1,then Which