Let y 1 , y 2 , … iid rvs with exponential distribution of parameter ?. Let x be a discrete rv…

Let y1, y2, … iid rvs with exponential distribution of parameter λ. Let x be a discrete rv defined as follows

where it is understood that x = 0 if y1 > 1. Prove that x has a Poisson distribution of parameter λ. Note that this method can be used for the computer-aided generation of instances of a Poisson distributed rv.