Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Homework Help
Calculus and Beyond Homework Help
Probability Density of Sum of Random Variables
Reply to thread
Message
[QUOTE="snipez90, post: 2400881, member: 100096"] [h2]Homework Statement [/h2] Suppose X and Y are independent random variables with X following a uniform distribution on (0,1) and Y exponentially distributed with parameter [itex]\lambda = 1[/itex]. Find the density for Z = X + Y. Sketch the density and verify it integrates to 1. [h2]Homework Equations[/h2] If Z = X + Y, and X and Y are independent, [tex]f_z(z) = \int_{-\infty}^{\infty}f_Y(z-x)f_X(x)\,dx[/tex] [h2]The Attempt at a Solution[/h2] I am trying to catch up on stats. I think I screwed up somewhere in this problem: If X ~ Unif(0,1), then [itex]f_X(x)[/itex] should just be 1 on (0,1) right? Also if the parameter of the exponential distribution is 1, then [itex]f_Y(z-x) = e^{-(z-x)}?[/itex] But then the expression for [itex]f_z(z)[/itex] doesn't seem to make much sense. Note I have no idea what I am doing. [/QUOTE]
Insert quotes…
Post reply
Forums
Homework Help
Calculus and Beyond Homework Help
Probability Density of Sum of Random Variables
Back
Top