# Exponential Distribution

#### norush

##### New Member
Let X and Y be independent exponential random variables with parameters λ and µ. Let Z = min{X, Y }.
a. (3 pts) Find P(X = Z).
So for this I calculated P(X=Z)=P(X<Y) and got the answer (λ/λ+µ)
b.Find P(Z>z)
Can anyone help me with how to go about doing this part of the question. Thank you

#### staassis

##### Active Member
Part a) is correct.

For part b, use the fact that Z is the interarrival time of the Poisson process which is the sum of the Poisson process corresponding to X and Poisson process corresponding to Y.