Poisson Processes

Question 1

poisson distrubutiins

Answer 1

distributions that arise when counting random events with key properties

1. events in disjoint time intervals are independent
2. the rate at which events occur does not depend on time

Question 2

processes and events of poisson

Answer 2

• radioactive decay = arrival of a particle at counter
• traffic flow on a minor road = car passing
• distribution of a plant in a field = plant

Question 3

for histograms described by Poisson distributions

Answer 3

mew = sigma squared

Question 4

poisson approximation to binomial

Answer 4

can be made if n is large and p is small enough and np<10
- when n is large and p is small, then X~B(n,p)
mew = np, sigma squared = np(1-p) = np = mew
X~Pois(n,p)

Question 5

if X has a Poisson distribution with mean mew and written X~poiss(mew)

Answer 5

then p(k) = (e^-mew mew^k)/k!
k is an integer