Are exponential random variables independent?
If we suppose that the amounts of time that it takes the item to pass through the successive stages are independent exponential random variables, and that the probability that an item that has just completed stage n quits the program is (independent of how long it took to go through the n stages) equal to r(n), then …
Is exponential distribution independent?
In probability theory and statistics, the exponential distribution is the probability distribution of the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate. …
What is the distribution of the maximum of n exponential random variables?
Below I’ve given a formula for the cumulative distribution function (CDF) of the maximum of n independent exponentials (which, of course, is one way to specify a distribution); if you want the density, you can differentiate it. It is fairly simple to first show the development for two independent exponentials, say X and Y with means and .
How to find the mean of the maximum of a random variable?
I am looking for the the mean of the maximum of N independent but not identical exponential random variables. I found the CDF and the pdf but I couldn’t compute the integral to find the mean of the maximum.
What is the distribution of two independent exponentials?
It is fairly simple to first show the development for two independent exponentials, say X and Y with means and . Their CDFs are I assume you mean independent exponential random variables; if they are not independent, then the answer would have to be expressed in terms of the joint distribution.
How to find the minimum of iid random variables?
Notice (prove for yourself), that the minimum of n iid exponential random variables follows an exponential distribution with mean 1 / ( n λ). Hence, we have E [ Z] = E [ Y 3 + Y 2 + Y 1] = E [ Y 3] + E [ Y 2] + E [ Y 1] = 1 3 λ + 1 2 λ + 1 λ = 1 λ ∑ k = 1 3 1 k.