18.44 Lecture Notes - Lecture 14: Random Variable, Stochastic Process, Philippine Standard Time
Document Summary
Properties from last time for integer k 0. A poisson random variable x with parameter satis es p{x=k} = The probabilities are approximately those of a binomial with parameters (n, /n) when n is very large. Many phenomena (number of phone calls or customers arriving in a given period, number of radioactive emissions in a given time period, number of major hurricanes in a given time period, etc. ) can be modeled this way. A poisson random variable x with parameter has expectation and variance . Special case: if =1, then p{x=k} = 1/(k!e) Note how quickly this goes to zero, as a function of k. Example: number of royal ushes in a million ve-card poker hands is approximately poisson with parameter. Example: if a country expects 2 plane crashes in a year, then the total number might be approximately poisson with parameter = 2.
