Summary Formulas and Distributions Probability Theory
5 views 0 purchase
Course
Probability Theory
Institution
Rijksuniversiteit Groningen (RuG)
Book
Introduction to Probability
This summary contains all formulas and distributions from chapter 1 till 6.3.
Deze samenvatting bevat de formules en de distributions van hoofdstuk 1 t/m 6.3
Bernoulli trial
An experiment (one single trial) that can result in either a success (1) or a failure (0).
X ~ Bern(p) with p being the probability of success.
With replacement Without replacement
Fixed number of Binomial Hypergeometric
trials Multiple trials with the same Urn filled with white and black balls,
success probability with X the then drawing n balls out with X being
number of successes. the number of white balls from the
sample.
X ~ Bin(n, p)
n -> number of trials X ~ HGeom(w, b, n)
p -> probability of success w -> number of white balls
b -> number of black balls
n -> number of draws
Fixed number of Negative Binomial Negative Hypergeometric
successes Multiple trials with the same Urn filled with white and black balls,
success probability with X the then drawing n balls out until r white
number of failures before the rth balls have been obtained with X being
success. the number of black balls drawn before
drawing the rth white ball.
X ~ NBin(r, p)
r -> number of successes X ~ NHGeom(w, b, r)
p -> success probability w -> number of white balls
b -> number of black balls
r -> number of wanted white balls
Discrete Uniform
Picking a random number from some finite set of numbers with equal probability.
X is the chosen number.
X ~ DUnif(C) with C the finite, nonempty set of numbers.
First Success
A sequence of independent Bernoulli trials, each with the same success probability, with trials
until the first successful trial, including the success.
Y is the number of trials until the first trial, including the success.
Y ~ FS(p) with p the success probability.
Geometric
A sequence of independent Bernoulli trials, each with the same success probability, with trials
performed until a success occurs.
X is the number of failures before the first successful trial.
X ~ Geom(p) with p the success probability.
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller katjakuijlaars. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $8.55. You're not tied to anything after your purchase.
