Expected Values for Continuous Variables!!!

If you ever muck around in statistics, it's not long before you see E(x) = something. These are expected values. Expected Values for Continuous Variables are a little trickier than their discrete counterparts because we have to do some calculus. However, I'll walk you through it, one step at a time, so don't sweat it! BAM!

NOTE: This one is, believe it or not, pretty near to my heart. When I was taking Statistical Theory in graduate school (from Rodger Berger of Casella and Berger, who wrote the standard textbook on statistical theory, "Statistical Inference") I remember having a lot of trouble with expected values. They intimidated me for two reasons 1) deriving them seemed like total luck and 2) I never understood, exactly, what the formula for continuous variables meant in a deep way. I could look at the equation and name the parts, but that was all I could do. Anyway, fast forward a few years and here I am, going back to these basics, this time determined to get that "deep understanding" I missed before, and, at least for myself, I succeeded. And I hope that means other people will also be able to get a deep understanding of expected values as well.

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0:00 Awesome song and introduction
1:30 Discrete and continuous variables defined
3:42 The exponential distribution
7:03 Approximating expected values with discrete intervals
10:25 Deriving the expected value formula for continuous variables
12:18 Calculating the expected value of an exponential distribution
18:17 Summary

#StatQuest

[theburtmacklin]

Amazing videos; if you only knew the way in which your channel had changed things for me… what started as a “hey this video looks cool” has largely been responsible for my wife enrolling into a data science postgrad program in the University of Waterloo.

[raulsena]

Amazing videos, just wanted to thank you for all you have taught me. Now I am doing a Master's Degree in Artificial Intelligence and planned to do a Ph.D. and all thanks to your videos.

[iroikoarakide]

Why do I have to attend college classes when you explain these concepts so thoroughly and in a third of the time? Great video as always man you are a Godsend

[otavioaugustodeassuncao]

Currently i'm studying Statistics at Federal University of São Carlos (UFScar) and just wanted to thank you for all the helpful and fun content that you've been posting... Not only had helped me to understand but also has made me like Statistics even more

[ahmadatta]

I'm in the library and I did not realize my laptop speaker was on, and the video started, as always, with a song. :D
I'm not even embarrassed. Everybody should hear your songs, they are amazing haha

[josherickson]

Triple bam bro! Now just need to refresh some calculus :)

[MrDanituga]

One of the best explanations I have ever had! Congratulations on the video and on your content in general. Watch every video :D

[norukamo]

Just discovered this channel an hour ago and now I'm binging your videos. They're soo good and easy to understand. BAM!

[zalavadiaridham]

Amazing video josh!!! I'm waiting for the video on why we divide by n-1 when we compute the sample variance. Thank you for the very informative content that you put out.

[newsupdates]

Double bam! Here to watch another great statquest video for a refresher <3

[durgeshkshirsagar]

You sound like kids' rhymes but when you teach, teach like a pro.

[awaisjabbar]

Liked the video, before it even starts, awesome channel, why I have not heard of you before.

[fedos]

I think I've had too much to drink, because I read the notification as "Star Quest with Josh Starmer", and I was confused about your sudden shift to astronomy. I'm going to have to watch this tomorrow.

[jerrycheung]

Great video! May I ask where is the next video to go to for solving the n - 1 puzzle?

[eduquest]

Thanks a lot dear, may god bless you Josh.

[kakashisensei]

Josh, I'm really thankful to all your vdos, it's enlightening, lol.
Please can you make some vdos on distribution functions (e.g., normal distribution)?

[Letsbetog]

You are an awesome singer As well as A great Teacher.🙃🙃🙃

[Altamira_]

Thanks for all of your videos they are great. I'm waching the full playlist "statistics fundamentals" and have to admit that since I understood all of the previous videos thanks to your great explanations I was lost on this one when you used integrals :/ I think it's the video that requires the more calculcus knowledge.

[mandaltech]

Waiting for your book. You area real teacher.

[alexandersmith]

Hi Josh. What video(s) after this should I watch to get closer to understanding why we divide by (n – 1) when finding the sample variance and sample covariance? An intuitive explanation for this seems nowhere to be found across the entirety of the internet, and the StatQuest channel has thus far been a divine gift of comprehension.