Chapter 5.4 STATS: Geometric & Poisson Distribution (when to use which formula and more!)

How is Binomial Distribution different from Geometric Distribution???

In geometric distribution, the random variable n represents the number of the trial on which the FIRST SUCCESS occurs (n=1,2,3,4....) In binomial distribution, the random variable r represent the number of successes of of n trials. (0 is less than or equal to r, which is less than or equal to n)

How is this different from the first two distributions?

It is a very good approximation to the binomial distribution, provided the number of trials n is larger than or equal to 100 and lambda L = np is less than 10.

Binomial Distribution is used when...

There are n trials and each are repeated under IDENTICAL conditions. This means that each trial has 2 outcomes: success or failure

Geometric Distribution is used when...

There are n trials and each are repeated under the same/IDENTICAL conditions. Each trial has 2 outcomes: success or failure

Poisson Distribution is used when...

a random process occurs over an amount of time, volume, area, or any other quantity that can (in theory) be subdivided into smaller and smaller intervals. The random variable r represents the number of successes that occur over the interval on which you perform the random process (r = 1,2,3,4,.....)

Poisson Approximation is used when...

there are n independent trials that are each repeated under identical conditions The random variable r represents the number of successes out of n trials in a binomial distribution

How do I find Mean (u) and standard deviation (o-) for a geometric distribution?

u = 1/p and o- = square root(q) / p The probability that the first success occurs on the nth trial is.... P(n) = pq^n-1

How do I find Mean (u) and standard deviation (o-) for a poisson distribution?

u = lambda (l) and o- = square root (l) The probability of r successes n the interval is P(r) = e^-l x (l)^r / r!

How do I find Mean (u) and standard deviation (o-) for a binomial distribution?

u = np (n trials x probability) o- = square root(npq) (q = 1-p) The probability of exactly r successes out of n trials is... C(little)n,r P^r (q)^n-r