Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Statistics 270 - Lecture 11 • Last day/Today: More discrete probability distributions • Assignment 4: Chapter 3: 5, 7,17, 25, 27, 31, 33, 37, 39, 41, 45, 47, 51, 65, 67, 77, 79 Poisson Distribution • A random variable, X, has a Poisson distribution with parameter l (l>0) if the pmf is • For x=0, 1, 2, … Poisson Distribution • Is this a pmf? Poisson Distribution • E(X) • V(X) Poisson Distribution • Observations: Example • Suppose the number of drivers who travel between a particular origin and destination during a designated time period has a Poisson distribution with parameter l=20 • Find the probability that ten drivers are observed • Find the probability that at most 10 drivers are observed Poisson Approximation to the Binomial • Suppose that the random variable X has a Bin(N,p) distribution and n!1 and p!0 so that np=l. The Bin(n,p) ! Pois(\lambda). • So, in any binomial experiment where n is large and p is small then the binomial distribution is approximately the same as the Poisson distribution where l=np • Can us Poisson distribution to compute binomial probabilities Poisson Approximation to the Binomial • Proof: Poisson Approximation to the Binomial • Rule of thumb: Example • A rare blood disease occurs in a population with frequency 0.001 • If n people are tested, what is the probability that at least two have the rare disease Example • n=100 • n=1000