Homogeneous poisson point process

Question

Assignment:

Q1. Show that the time interval between two events in a homogeneous Poisson point process with intensity Ahas an exponential distribution with mean I/λ.

Q2. If N₁ and N₂ are independent homogeneous Poisson point processes (HPPP) with intensities λ₁ and λ₂, show that N = N₁ + N₂ is HPPP with intensity
λ = λ₁ + λ₂

Your answer must be, typed, double-spaced, Times New Roman font (size 12), one-inch margins on all sides, APA format and also include references.