# 1.2 The Expected Value and Variance of Discrete Random Variables

An introduction to the concept of the expected value of a discrete random variable.

I also look at the variance of a discrete random variable. The formulas are introduced, explained, and an example is worked through.

This is an updated and refined version of an earlier video. Those looking for the original version can find it at http://youtu.be/OvTEhNL96v0.

### 10 thoughts on “1.2 The Expected Value and Variance of Discrete Random Variables”

1. Hi, Great Videos. How did you simulate one million times and obtain relative frequency in the “novelty coin” example stated in the “An introduction to the concept of the expected value of a discrete random variable” ?

Srini

• Thanks! All of my simulations and plots were done in R.

2. hi,

my compliments for the great videos! Have been teaching stats for the humanities (corpus linguistics) and recently found out about this great series and this semester am planning to refer to them in my class. Keep up with the good work! One suggestion would be to show us some videos about stat models for count data.

Thanks a lot again!

• Hi Alex.

Thanks for the kind words! And thanks for the suggestion. I’ll keep it in mind when I get back to video production. (I’ll find the time one of these years!)

All the best.

Jeremy

3. Thanks for your videos! You are so helpful, JB. Thank you so much.
– Happy stats student (Charlotte)

• You are very welcome Charlotte!

4. Hey JB,

These videos are amazing. Thank you for them!!

-Brendan

• You are very welcome. And thanks!

5. Hey JB,
I really like you videos. In this video you explain how to calculate the expected value, variance and standard deviation. The question is why we are interested in calculating variance and standard deviation. what information do we gain from calculating these values in real world applications?
once again thanks for your great videos.

• Hi Sourena,

The variance and standard deviation are commonly used measures of variability. In practical applications, they are used as descriptive measures of variability, and can help us quickly estimate probabilities (e.g. “that observation is 4 standard deviations about the mean — there’s only a small chance of seeing something like that.”) The sample versions are used statistical inference procedures when creating confidence intervals and carrying out hypothesis tests. Cheers.