Statistics 101: Discrete Random Variable Variance
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- Опубликовано: 12 июл 2024
- Statistics 101: Discrete Random Variable Variance.
In this video, we continue our discussion of expected value. The expected value is simply the mean of a random variable. However, that does not tell you how spread out or dispersed the probabilities are from the mean. If you have ever calculated a weighted average you can easily calculate random variable variance. Several practical and concrete examples are provided. Enjoy!
My playlist table of contents, Video Companion Guide PDF documents, and file downloads can be found on my website: www.bcfoltz.com
The super nerd in me loved this video as a refresher video before a cumulative stats exam. THANK YOU!
Sir you are one hell of an instructor...great articulation skills
you are the best.you only give out what is essential!AWESOME
Many thanks for these nice lectures.
These videos are great! I'm taking a statistics and probability course for extra credit right now but I don't have the time to go to class so I'm studying on the weekends. This will help me get a 5 out of 5 on the exam (swedish grading system) . Thank you!
5 av 5? Var exakt har man det?
Thanks again!
your way of teaching is good
GREAT!!!
Can you double check the calculations of the class satisfaction variance for x=5, with P(x) =.351. For (x-u)2P(x) = I got .351 x 1.69 =.593 not .488. ???
It's skewed left, not right. Right?
yes
I love your videos ! In which order i have to see your videos to learn statistics ?
Thanks Brandon for all that you do. I did the calculation myself and found these Mean - 3.93, Var - 1.24, StDev - 1.11. However, my question here was how can I get this done in Minitab. Need help with this one. Any response from any one would be appreciated. Thank you
Same calculation results turned out for me
Excellent
Brandon, thanks for the amazing video. But I've never saw the variance equation to contain this *P(x) at the end before. I always saw it as the sum of (x - mu)^2 divided by the number of observations. Is this not the same thing? In the die roll example we would get to 2,92 at the end too if we just had divided by six.
superb
Thank you. Do you go on to explain the Expected Value of Function of a Random Variable and the Linear Function?
I did not get an expected value of 3.70 I got 3.92 while I added them all up...what at I doing wrong?
+Selina Benoit nothing. 3.92 is correct. there is a rounding error in the video.
=)
Also got 3.92
IS it just me or should the Standard Deviation in the last question be 1.71 not 1.09?
Some constructive criticism:
at 20:46 for example, in the 5th column, last two rows, you write out (sigma)^2 and (sigma). It confused me quite a bit first because I thought you meant that (sigma)^2 = (x - u)^2 , which isn't consistent with the formula stated at the very bottom. A quick explanation in the video would be helpful :) .
🎯 Key Takeaways for quick navigation:
01:00 *🎲 Introduction and overview of the video content*
- Video aimed at individuals new to Stats or finite mathematics
- Concepts in the video applicable to both statistics and finite mathematics
- Focus on extending the discussion on discrete random variables to variance and standard deviation
02:27 *🔍 Understanding the variability in random variables through variance and standard deviation*
- Variance and standard deviation measure the spread of data from the mean
- Importance of variance in making statistical assumptions about data
- Use of variance in comparing data sets and drawing conclusions
04:07 *📊 Equation and calculation of variance explained*
- Breakdown of variance calculation formula
- Importance of understanding each step in the variance calculation process
- Application of the variance formula to discrete random variables
08:22 *🎲 Example with a die roll and calculation of mean, variance, and standard deviation*
- Mean of a die roll explained
- Calculation process for variance in a die roll scenario
- Relationship between variance, standard deviation, and the mean in the context of a die roll
11:36 *📈 Example with class satisfaction surveys and calculation of variance and standard deviation*
- Calculation of variance in the context of class satisfaction surveys
- Interpretation of variance and standard deviation in relation to expected value
- Visual representation of probability distribution skewed towards higher satisfaction levels
Made with HARPA AI
shouldn't you be dividing by the sample size (n) to the sum for variance and std dev?
Hello Mohsin! For discrete random variables the variance and standard deviation are different than for continuous. It is based on the expected value and probability of each discrete outcome; very much like "weighting" each discrete outcome. What I am pretty sure you are thinking about are continuous random variables as opposed to discrete. Hope that helps! - B
***** thank you sir
+Brandon Foltz I was seeing the video on the same topic on a channel named jb statistics in which he says 'expected value' is not the same as mean. The expected value we calculate thru 'adulteration' [ i.e we first calculate probability and then multiply with outcomes etc ] while the simple mean we calculate simply without the values of the problem being adulterated. So, I feel the proper word wud be apparent mean. What are ur thoughts on it.
here is the link for that video.
@@BrandonFoltz I think - this is not because of descrete or not, but because of probability - in probability we devide every time by total number of events, i.e. in probability embeded devision by N.
In class satisfaction variance example how mean is calculated as 3.7...and can u please let me know that do you have any book for all these videos???
Why would it be combination but not permutation to calculate the different groups of successes since where the failures are in the trial matters? So the order of the failure and success matter, but why isn't it permutation?
Would SD or Variance be a valid measure on such skewed data?
No, only for normal distribution.
Just something I noticed variance should be denoted as Var(X) instead its denoted as Var(x)