Class Notes (838,348)
Canada (510,861)
Statistics (475)
STAT 330 (53)
Lecture

Joint distributions handout.pdf

1 Page
85 Views
Unlock Document

Department
Statistics
Course
STAT 330
Professor
Christine Dupont
Semester
Fall

Description
Joint Distributions Suppose X and Y are defined on the same sample space S. 1. Joint c.d.f.: F(x;y) = P(X ▯ x;Y ▯ y) 2. Properties of F: (a) For fixed x, F is non-decreasing in y (b) For fixed y, F is non-decreasing in x (c) lim F(x;y) = 0 and lim F(x;y) = 0 x!▯1 y!▯1 (d) lim F(x;y) = 0and lim F(x;y) = 1 (x;y)!(▯1;▯1) (x;y)!(1;1) 3. (a) Marginal c.d.f. of X:x) = P(X ▯ x) = y!1 F(x;y) = F(x;1) (b) Marginal c.d.f. of Y:y) = P(Y ▯ y) = lim F(x;y) = F(1;y) x!1 4. Joint Discrete Random Variables (Suppose the sample space S is discrete): (a) Joint p.f.: f(x;y) = P(X = x;Y = y). Support set A = f(x;y) : f(x;y) > 0g (b) Properties of f: 2 i. f(x;y) ▯ 0 8(x;y) 2 R X X ii. lim F(x;y) = f(x;y) = 1 (x;y)!(1;1) (x;y)A
More Less

Related notes for STAT 330

Log In


OR

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Sign up

Join to view


OR

By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.


Submit