Probability Distributions Flashcards
Under what conditions is the Poisson distribution valid?
- The events must occur randomly
- The events must be independent of each other
- The average rate of the events must be constant
What does the geometric distribution model?
The random variable: number of trials up to and including the first success
What conditions must hold for the geometric distribution to be valid
- There are trials where all outcomes can be classified into two distinct categories
- The trials are independent
- The probability of success, p, is constant for each trial
- There is no upper limit to the number of trials
For a geometric distribution, what does P(X>x) = ?
P(X>x) = (1-p)^x
What are the key phrases in a question which indicate you should use a Poisson distribution?
- Average rate of events
- Events occuring at a constant rate
- NEVER a fixed number of trials
What properties of your data indicate the Poisson might be a good model?
The mean and the variance are roughly equal (and therefore the standard deviation is the square root of this)
If the number of butterflies seen in 10 minutes is x and you are using a poisson to model the number of butterflies in 1 hour, what is λ?
λ = 6x
What can be said about the sum of two independent variables which both follow a Poisson distribution?
If two independent variables both follow a Poisson distribution, then so does their sum.