# Exponential Probabilities

1. Sep 23, 2009

### oscaralive

1. The problem statement, all variables and given/known data

Let <d1,d2,d3...dN> be an odered set of samples from an exponential
random variable with parameter lambda.
Let <l1,l2,l3,...,lM> the same.

Let Z = min<d1,d2,...,dN> --> Z is exp with parameter lambda*N
Let U = min<l1,l2,...,lM> --> U is exp with parameter lambda*M

2. Relevant equations

Since we can write that:
p(Z > U) = M/(N+M), which is in fact, p(d1 > l1)= p(Z > l1)

How can I compute the following probability:

p(Z > l2), p(Z > l3),...,p(Z > lN).

3. The attempt at a solution

Until now I am "approximating" this probability by assuming that:

p(Z > l2) = (M-1)/((M-1)+N) and succesively, but I know it is wrong....