yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Valid discrete probability distribution examples | Random variables | AP Statistics | Khan Academy


3m read
·Nov 11, 2024

Anthony Denoon is analyzing his basketball statistics. The following table shows a probability model for the result from his next two free-throws, and so it has various outcomes of those two free-throws and then the corresponding probability: missing both free-throws 0.2, making exactly one free-throw 0.5, and making both free-throws 0.1. Is this a valid probability model?

Pause this video and see if you can make a conclusion there.

So let's talk about what makes a valid probability model.

  1. The sum of the probabilities of all the scenarios needs to add up to 100%. So we would definitely want to check that.

Also, they would all have to be positive values, or I guess I should say none of them can be negative values. You could have a scenario that has a 0% probability, and so all of these look like positive probabilities. So we meet that second test that all the probabilities are non-negative.

But do they add up to 100%? So if I add 0.2 to 0.5, that is 0.7, plus 0.1, they add up to 0.8, or they add up to 80%. So this is not a valid probability model.

In order for it to be valid, all the various scenarios need to add up exactly to 100%. In this case, we only add up to 80%. If this had added up to 1.1 or 110%, then we would also have a problem. But we can just write no.

Let's do another example.

So here we are told, "You are a space alien. You visit Planet Earth and abduct 97 chickens, 47 cows, and 77 humans. Then you randomly select one Earth creature from your sample to experiment on. Each creature has an equal probability of getting selected. Create a probability model to show how likely you are to select each type of Earth creature. Input your answers as fractions or as decimals rounded to the nearest hundred."

So in the last example, we wanted to see whether the probability model was valid, was legitimate. Here, we want to construct a legitimate probability model.

Well, how would we do that? Well, the estimated probability of getting a chicken is going to be the fraction that you're sampling from. That is, our chickens, because any one of the animals is equally likely to be selected.

There are 97 of the 97 plus 47 plus 77 animals that are chickens. So what is this going to be? This is going to be 97 over 97, plus 47, plus 77. You add them up: three sevens is 21.

Then let's see: 2 plus 9 is 11, plus 4 is 15, plus 7 is 22, so 221. So 97 of the 221 animals are chickens.

I'll just write 97 over 221. They say that we can answer as fractions, so I'm just going to go that way.

What about cows? Well, 47 of the 221 are cows, so there’s a 47 over 221 probability of getting a cow.

And then last but not least, you have 77 of the 221 are humans.

Is this a legitimate probability distribution? We'll add these up. If you add these three fractions up, the denominator is going to be 221, and we already know that 97 plus 47 plus 77 is 221.

So it definitely adds up to 1, and none of these are negative, so this is a legitimate probability distribution.

More Articles

View All
Catch of the Week - Burn Blubber | Wicked Tuna: Outer Banks
[Music] That bird is up there waiting to get a little snack. All right guys, I got a more need to bite. Boy, need to bite bad! We’re on! We’re on! R on! Let’s get him! It’s going to be a nice one, baby! Look at that! Mark, that’s what you want right ther…
Cosplay, ILLUSIONS, and Pacman: IMG! 7
If Pac-Man was a real living organism and party time—wait, what? [Music] We start today like I start every day, wrapped up in covers. Oopah brought us some great bedspreads. This one would make me feel less lonely. This one’s great for parties, and this…
Answering Google's Most Asked Questions of 2022
For most of Google’s relatively short existence, we’ve searched small, silly, insignificant questions - things like how to tell if a papaya is ripe. The color is almost fully yellow, and the feeling is slightly soft. Don’t forget to scoop out the seeds! S…
Brown v. Board of Education of Topeka | US government and civics | Khan Academy
[Kim] Hi, this is Kim from Khan Academy, and today we’re learning more about Brown v. Board of Education of Topeka. Decided in 1954, Brown v. Board was a landmark case that opened the door for desegregation and the Modern Civil Rights Movement. In Brown, …
What Hermes Taught MeQT
Hi, Kevin O’Leary, investor at large. I’ve just come back from a shopping trip and learned a very important lesson. You know I love Hermès fantastic ties. What I hate about them is the price. So, I like to shop for volume, see if I can get a discount. I…
Geometric constructions: perpendicular line through a point off the line | Geometry | Khan Academy
What I have here is a line, and I have a point that is not on that line. My goal is to draw a new line that goes through this point and is perpendicular to my original line. How do I do that? Well, you might imagine that our compass will come in handy; i…