read more
Study for Final 


Exponential distribution: P(a,b) = e^-lamba*a - e^-lambda*b. Which is same as integral of lambdae^-lambda*x from a to b. 

Poission distribution: lambda*k e^-lambda / k! for k is integer. This for “what is probability that there are k arrivals given lambda and that it’s poisson”. You can get intervals from this by summing k’s. (so if you wanted probability that it was (8-10), you would plug in k=8,9,10 and add them. 

Binomial distribution: (n choose x) p^x q^n-x. x must be integer. Sum across x’s to get probability of intervals. 


For discrete distributions, there is typically no way to write the CDF with a formula. Just write each value down. 

For continuous, just evaluate the integral of the density from zero to x. That should be your CDF. 


Poission process any interval [t,t+s], number of arrivals is p(x) = (lambda*s)^x*e^-lambda*s/x!. (p173). 

For any point t, waiting time from t to next arrival is lambda*e^-lambda*t.