Superposition, Thinning, Conditioning and Higher Dimensions

Superposition and thinning

Conditioning on a shared count

Spatial Poisson processes

Independent processes of rates 2 and 5 merge. What is the merged stream?

A rate-6 process thins with p = 1/3 to type 1. What is the type-1 process?

Two independent processes of rates 1 and 2 per hour merge. What is P(no arrivals in a 30-minute window)? Use e^(-1.5) is about 0.223. Enter like 0.223.

A merged stream of rates 2 and 6 has exactly 4 arrivals in a window. The number of type-1 (rate-2) arrivals is Binomial(4, p). What is p? Enter a fraction like 1/4.

Stars scatter at intensity 40 per square degree. P(no star within radius 0.1 degrees of a point) is e to the minus 40 pi times 0.1 squared. Using pi about 3.14, compute the exponent's value, like 1.26.

In your own words, state the most important definition, theorem or method of this lesson and explain what it says.