Question

Let X and Y be independent exponential random variables with respective rates ? and ? Is max(X, Y ) an exponential random variable?

Answer 1

Answer:

Given that:

Let X and Y be independent exponential random variables with respective rates ? and ? Is max(X, Y ) an exponential random variable?

Given ,  

Let Z = min(X,Y)

To find distribution of Z ,we find cdf of Z

   X and Y are independent

  

cdf of Z has exactly the form of cdf exponential distribution

variable Z is also a exponential i,e min(X,Y) is a exponential variable.