Summary
Summary Intro to probability distributions and related concepts
- Institution
- Stellenbosch University (SUN)
This material covers introductory statistical concepts, such as bivariate distributions and moment-generating functions.
[Show more]
Connected book
Book Title:
Author(s):
- Edition:
- ISBN:
- Edition:
Seller
Follow
Content preview
Whatis a multivariate probabilitydistribution?
Probabilities involving multiple with
leach
events a distribution occurring together, i.e.
the probability ofthe intersection of events.
↳
For example:P ( Y, y,) and P(Yc
=
yc)
=
and ... and PLYn yn)
=
P(X, y,,yz
=
= =
y2, ..., Yu yn)
=
or more compactly, P(y,y,,..., yn).
* joint probability
distribution.
It'slike calculating multiple individual probabilities simultaneously.
Where would multivariate distributions be used?
When we wantto investigate thatconsist
events ofmultiple individual events
occuring together.
the marginal distributions
given
How do we find the jointdistribution function?Does indepence ofthe random
1
variables
play a role?
In
general, you can't find the jointdistribution from the
marginal distributions,
unless thatthe variables independent, in which
you are
given are case
fxy(x,y) fx(x).fy(y).
=
For
jointdistributions of dependentvariables, see copulas and solar's theorem
, 40,
EX 5.14
by,"y,, 0
y,2y2,y, y22
f(y,,y2)
+
=
elsewhere.
joint density function, ssfleieldyet
(a)To be a valid
Ye 1
:"
Sy-sysyndy,dy, o.
giydyzdy, =
0
(yi (702)?") dy,
6(yp[z(z y,) - 1(3)"]dy,
=
-
6.y?(z(4
=
-
4y, y,)
+ -
typ]dy,
iyi (z
=
-
zy, +
typ -
zyp]dy,
=
6(2y, -
2ypdy,
12fyi y3dy,
=
-
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 EFT, 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 this summary from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller tanweerkola. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy this summary for R100,00. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
67474 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy summaries for 14 years now