Transcription of Examples: Joint Densities and Joint Mass Functions
{{id}} {{{paragraph}}}
Example: confidence
Examples: Joint Densities and Joint Mass Functions
AMS 311 Joe MitchellExamples: Joint Densities and Joint mass FunctionsExample 1:XandYare jointly continuous with Joint pdff(x, y) = cx2+xy3if 0 x 1, 0 y 20,otherwise.(a). Findc. (b). FindP(X+Y 1). (c). Find marginal pdf s ofXand ofY. (d). AreXandYindependent (justify!). (e). FindE(eXcosY). (f). Findcov(X, Y).We start (as always!) by drawing the support set. (See below, left.)21211y=1 xxyxysupport setBlue: subsetof support setwith y>1 x(a). We findcby setting1 =Z Z f(x, y)dydx=Z10Z20(cx2+xy3)dydx=2c3+13,soc= 1.(b). Draw a picture of the support set (a 1-by-2 rectangle), andintersect it with the set{(x, y) :x+y 1}, which is the region above the liney= 1 x. See figure above, compute the probability, we double integrate the Joint density over this subset of thesupport set:P(X+Y 1) =Z10Z21 x(x2+xy3)dydx=6572(c).
AMS 311 Joe Mitchell Examples: Joint Densities and Joint Mass Functions Example 1: X and Y are jointly continuous with joint pdf f(x,y) = ˆ cx2 + xy 3 if 0 ≤ x ≤ 1, 0 ≤ y ≤ 2
Loading..
Tags:
Information
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document:
Related search queries
Is a subspace of, And nd a basis of, HOW TO SELECT AND PROPERLY USE WIRE, MATH 214 { QUIZ 12 { SOLUTIONS, 20D - Homework Assignment 0, 20D Homework Assignment 0, 20D - Homework Assignment 0 1, Coding Dermatology Procedures, 1 Z-Transforms, Their Inverses Transfer or, 1. Given the relation, Understanding SWR by Example, 1 0 0 1, 1 Review of Probability, Columbia University