# The Minimum of Two Independent Geometric Random Variables

Let H be a random variable with probability p1 that has a Geometric distribution G1 Let Y be a random variable with probability p2 that has a Geometric distribution G2

H and Y are two independent geometric random variables.

What is distribution of Z =min(H,Y)

© BrainMass Inc. brainmass.com October 10, 2019, 1:42 am ad1c9bdddfhttps://brainmass.com/math/discrete-structures/minimum-two-independent-geometric-random-variables-345248

#### Solution Summary

This problem shows in detail that the minimum of two independent geometrically-distributed random variables is itself geometrically distributed.

$2.19