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 6 hours ago Russia Invades Ukraine View the latest post Replies 643 Views 209053
- by Eli 6 hours ago Collection of Greatest Christian Hymns of all Times View the latest post Replies 30 Views 42689
- by Eli 9 hours ago All in One: YouTube, TED, X, Facebook and Instagram Reels, Videos, Images and Text Posts View the latest post Replies 273 Views 6506
- by Eli 1 day ago Chat With ChatGPT - An Interactive Conversational AI View the latest post Replies 21 Views 22668
- by Eli 5 days ago Re: What is in Your Mind? View the latest post Replies 658 Views 271364
- by Eli 6 days ago Mission Control Live: NASA InSight Mars Landing Live Coverage View the latest post Replies 32 Views 12960
- by Eli 6 days ago Christian Podcasts View the latest post Replies 4 Views 28279
- by Eli 1 week ago Python Packages for Scientific Computing View the latest post Replies 7 Views 2713
- by Eli 1 week ago Pondering Big Cosmology Questions Through Lectures and Dialogues View the latest post Replies 32 Views 44705
- by Eli 2 weeks ago C++ PROGRAMMING CRASH COURSE View the latest post Replies 4 Views 1290
-
Pdf and cdf of a continuous random variable
-
- Information
-
Who is online
Users browsing this forum: No registered users and 0 guests