A continuous random variable has a pdf of the form
$f(x)=\begin{cases}ce^{-2x}&x>1\\0&x\leq1,\end{cases}$where is a constant. Find the value of and the cdf of .
If is a pdf, then we must have , so we simply need to solve for the value of . That is,
$\int_{-\infty}^\infty f(x)\,dx$ $=\int_{-\infty}^\infty ce^{-2x}\,dx$ $=\int_1^\infty ce^{-2x}\,dx$ $=\left.-\frac{c}{2}e^{-2x}\right|_{x=1}^\infty$ $=\frac{c}{2}e^{-2}=1\Rightarrow c=2e^2.$
Then the cdf of is
-
- Active Topics
-
-
- by Eli 11 hours ago Re: What is in Your Mind? View the latest post Replies 697 Views 287391
- by Eli 1 day ago Russia Invades Ukraine View the latest post Replies 655 Views 223149
- by Eli 2 days ago Collection of Greatest Christian Hymns of all Times View the latest post Replies 34 Views 56232
- by Eli 2 days ago Pondering Big Cosmology Questions Through Lectures and Dialogues View the latest post Replies 34 Views 57512
- by Eli 4 days ago Programmatically Manipulate Files: Renaming, Reading, Writing, Deleting, and Moving Files Between Folders View the latest post Replies 7 Views 5364
- by Eli 1 week ago Iran Launches Retaliatory Attack Against Israel, and Israel Retaliates by Attacking Iranian Isfahan Millitary Base View the latest post Replies 28 Views 4866
- by Eli 1 week ago All in One: YouTube, TED, X, Facebook and Instagram Reels, Videos, Images and Text Posts View the latest post Replies 319 Views 22330
- by Eli 1 week ago Python Packages for Scientific Computing View the latest post Replies 8 Views 11495
- by Eli 1 week ago Dunia Yetu: Building Tanzania's Digital Future Together View the latest post Replies 5 Views 2340
- by Eli 3 weeks ago What is Retrieval-Augmented Generation (RAG)? View the latest post Replies 2 Views 4059
-
Pdf and cdf of a continuous random variable
-
- Information
-
Who is online
Users browsing this forum: No registered users and 0 guests