We already know a little

bit about random variables. What we’re going to

see in this video is that random variables

come in two varieties. You have discrete

random variables, and you have continuous

random variables. And discrete random

variables, these are essentially

random variables that can take on distinct

or separate values. And we’ll give examples

of that in a second. So that comes straight from the

meaning of the word discrete in the English language–

distinct or separate values. While continuous– and I

guess just another definition for the word discrete

in the English language would be polite, or not

obnoxious, or kind of subtle. That is not what

we’re talking about. We are not talking about random

variables that are polite. We’re talking about ones that

can take on distinct values. And continuous random

variables, they can take on any

value in a range. And that range could

even be infinite. So any value in an interval. So with those two

definitions out of the way, let’s look at some actual

random variable definitions. And I want to think together

about whether you would classify them as discrete or

continuous random variables. So let’s say that I have a

random variable capital X. And it is equal to–

well, this is one that we covered

in the last video. It’s 1 if my fair coin is heads. It’s 0 if my fair coin is tails. So is this a discrete or a

continuous random variable? Well, this random

variable right over here can take on distinctive values. It can take on either a 1

or it could take on a 0. Another way to think

about it is you can count the number

of different values it can take on. This is the first

value it can take on, this is the second value

that it can take on. So this is clearly a

discrete random variable. Let’s think about another one. Let’s define random

variable Y as equal to the mass of a random

animal selected at the New Orleans zoo, where I

grew up, the Audubon Zoo. Y is the mass of a random animal

selected at the New Orleans zoo. Is this a discrete

random variable or a continuous random variable? Well, the exact mass–

and I should probably put that qualifier here. I’ll even add it here just to

make it really, really clear. The exact mass of a random

animal, or a random object in our universe, it can take on

any of a whole set of values. I mean, who knows

exactly the exact number of electrons that are

part of that object right at that moment? Who knows the

neutrons, the protons, the exact number of

molecules in that object, or a part of that animal

exactly at that moment? So that mass, for

example, at the zoo, it might take on a value

anywhere between– well, maybe close to 0. There’s no animal

that has 0 mass. But it could be close to zero,

if we’re thinking about an ant, or we’re thinking

about a dust mite, or maybe if you consider

even a bacterium an animal. I believe bacterium is

the singular of bacteria. And it could go all the way. Maybe the most massive

animal in the zoo is the elephant of some kind. And I don’t know what it

would be in kilograms, but it would be fairly large. So maybe you can

get up all the way to 3,000 kilograms,

or probably larger. Let’s say 5,000 kilograms. I don’t know what the mass of a

very heavy elephant– or a very massive elephant, I

should say– actually is. It may be something

fun for you to look at. But any animal could have a

mass anywhere in between here. It does not take

on discrete values. You could have an animal that

is exactly maybe 123.75921 kilograms. And even there, that actually

might not be the exact mass. You might have to get even

more precise, –10732. 0, 7, And I think

you get the picture. Even though this is the

way I’ve defined it now, a finite interval, you can take

on any value in between here. They are not discrete values. So this one is clearly a

continuous random variable. Let’s think about another one. Let’s think about– let’s say

that random variable Y, instead of it being this, let’s say it’s

the year that a random student in the class was born. Is this a discrete or a

continuous random variable? Well, that year, you

literally can define it as a specific discrete year. It could be 1992, or it could

be 1985, or it could be 2001. There are discrete values

that this random variable can actually take on. It won’t be able to take on

any value between, say, 2000 and 2001. It’ll either be 2000 or

it’ll be 2001 or 2002. Once again, you can count

the values it can take on. Most of the times that

you’re dealing with, as in the case right here,

a discrete random variable– let me make it clear

this one over here is also a discrete

random variable. Most of the time

that you’re dealing with a discrete random

variable, you’re probably going to be dealing

with a finite number of values. But it does not have to be

a finite number of values. You can actually have an

infinite potential number of values that it

could take on– as long as the

values are countable. As long as you

can literally say, OK, this is the first

value it could take on, the second, the third. And you might be counting

forever, but as long as you can literally

list– and it could be even an infinite list. But if you can list the

values that it could take on, then you’re dealing with a

discrete random variable. Notice in this

scenario with the zoo, you could not list all

of the possible masses. You could not even count them. You might attempt to–

and it’s a fun exercise to try at least

once, to try to list all of the values

this might take on. You might say,

OK, maybe it could take on 0.01 and maybe 0.02. But wait, you just skipped

an infinite number of values that it could take on, because

it could have taken on 0.011, 0.012. And even between those,

there’s an infinite number of values it could take on. There’s no way for you to

count the number of values that a continuous random

variable can take on. There’s no way for

you to list them. With a discrete random variable,

you can count the values. You can list the values. Let’s do another example. Let’s let random

variable Z, capital Z, be the number ants born

tomorrow in the universe. Now, you’re probably

arguing that there aren’t ants on other planets. Or maybe there are

ant-like creatures, but they’re not going to

be ants as we define them. But how do we know? So number of ants

born in the universe. Maybe some ants have figured

out interstellar travel of some kind. So the number of ants born

tomorrow in the universe. That’s my random variable Z. Is

this a discrete random variable or a continuous random variable? Well, once again, we

can count the number of values this could take on. This could be 1. It could be 2. It could be 3. It could be 4. It could be 5 quadrillion ants. It could be 5 quadrillion and 1. We can actually

count the values. Those values are discrete. So once again, this

right over here is a discrete random variable. This is fun, so let’s

keep doing more of these. Let’s say that I have

random variable X. So we’re not using this

definition anymore. Now I’m going to define

random variable X to be the winning time– now

let me write it this way. The exact winning time for

the men’s 100-meter dash at the 2016 Olympics. So the exact time that it took

for the winner– who’s probably going to be Usain Bolt,

but it might not be. Actually, he’s

aging a little bit. But whatever the exact

winning time for the men’s 100-meter in the 2016 Olympics. And not the one that you

necessarily see on the clock. The exact, the

precise time that you would see at the

men’s 100-meter dash. Is this a discrete or a

continuous random variable? Well, the way I’ve defined, and

this one’s a little bit tricky. Because you might

say it’s countable. You might say, well,

it could either be 956, 9.56 seconds, or 9.57

seconds, or 9.58 seconds. And you might be

tempted to believe that, because when you watch the

100-meter dash at the Olympics, they measure it to the

nearest hundredths. They round to the

nearest hundredth. That’s how precise

their timing is. But I’m talking about the exact

winning time, the exact number of seconds it takes

for that person to, from the starting gun,

to cross the finish line. And there, it can

take on any value. It can take on any

value between– well, I guess they’re limited

by the speed of light. But it could take on any

value you could imagine. It might be anywhere between 5

seconds and maybe 12 seconds. And it could be anywhere

in between there. It might not be 9.57. That might be what

the clock says, but in reality the exact

winning time could be 9.571, or it could be 9.572359. I think you see what I’m saying. The exact precise time could

be any value in an interval. So this right over here is a

continuous random variable. Now what would be

the case, instead of saying the

exact winning time, if instead I defined X to be the

winning time of the men’s 100 meter dash at the 2016

Olympics rounded to the nearest hundredth? Is this a discrete or a

continuous random variable? So let me delete this. I’ve changed the

random variable now. Is this going to

be a discrete or a continuous random variable? Well now, we can actually

count the actual values that this random

variable can take on. It might be 9.56. It could be 9.57. It could be 9.58. We can actually list them. So in this case, when we round

it to the nearest hundredth, we can actually list of values. We are now dealing with a

discrete random variable. Anyway, I’ll let you go there. Hopefully this gives you

a sense of the distinction between discrete and

continuous random variables.

lol Yes, Usain won the 100m

thanks a lot,i was reading my course material and i did not understand anything.but with this video there is clarity and simplicity

Great video

Usain Bolt won though

I like the ant example.

Bolt did win right? Lol.

Thank u so much man, really appreciate it

Usain Bolt won though lol

Love how he called out Bolt would win in the 2016 Olympics!

This video helped me so much thank you wish you were my professor! thank you thank you thank you!!!!

استفدت كثيرا 👍+ صوتك رائع ما شاء الله. thank u so muce

You are a lot clearer than my teacher!

Great lesson and visuals! Thanks so much! 🙂

I didnt get the last part. Does this means if it is rounded up by nearest thousand, it will be a discrete rv? Does this means 9.56, 9.57, 9.57 are discrete?

WTF Sal grew up in a zoo!!!!!

2:36

bro, you grew up in a zoo?

XD

i know this sounds silly, but i think he's wrong Y is a discrete variable because it has a clear beginning and end. could some one help me understand or show me how I'm wrong. I just want to know? Also i do respect the guy his videos are awesome.

I´ve finally understood the difference thanks!

"We're not talking about random variables that are polite" LOL 😛

I personally think that Discrete random variable can be identified by a simple test as following, "If bound in a range given by two finite numbers, if the random variable takes infinite values then it cannot be a discrete random variable".

bolt 2016

Bacteria aren't animals tho.

Thanks a lot… I finally understood them.

Thank you khan academy very much 😍😍😍

bacteria are not animals :/

why do math teachers ALWAYS incorporate RANDOM stuff into the lessen just like he did with usain bolt and He's aging lol

my math teacher brought up a drawing she did when she was a kid for a geometry lesson 😂 it's kinda funny honestly

theory of randomness. new theory of random variables with accuracy of more than 90 %. or more. that is. principios de teoria del azar : cualquier clace de variables aleatorias siempre encontraremos cantidades no homogeneas. agrupacion irregular de datos. principio de.bipolarida, esto lo encontramos cuando tenemos valores medios de.vibracion de datos. las resultantes se pueden ir por igual monto tanto a valores positivos como negativos. en historic data estan los artificios matematicos para predecir.el futuro indudablemente. unfortunately for the.scientific community this theory and others are not available for usa. and therefore for no country. sorry

what if you don't know what the numbers represent? how then can you figure it out? is this set of values discrete {6,7,5,2,9,12,3,8} ? if so, why? what about this one? {3.14159, 2.71828, 1.61803, 1.41421, 0.37396} , would those be considered continuous because they are decimals?

He actually predicted the 100 m dash four years in advance :O Thats impressive

There are more numbers between 0 and 1

then from 0 to positive Infinity

In the lecture I attended, the teacher said the best way to tell the diference is to see if the numbers the random variable takes are natural numbers then it's likely a discrete variable, on the other hand if the value the random variable takes is a real number then it might be a continous random variable.

I'm still confused

thanks your a big help i hope you have input some test on your video

What about monthly expenditure

Space ants!! The Sandkings are coming 😱

Ants have already figured out interstellar travelling.

Illuminati confirmed.

I did not understand that 1 hour of math class teaching, and now it makes sense. Thank you!

what if the unverse is infinite, is the ants still a discrete rv?

When I read the textbook on this topic, it just made my brain literally hurt. But when Khan explained this same exact topic, I understood it completely and I swear my brain relaxed.

Basically , an event having whole no.as a value it's discrete and a decimal value is a continuous 😎

ARIGATO I NEEDED THIS LESSON FOR MY PROJECT

Because of QM, both exact mass and exact time are discrete. Which begs the question, are there any physical continuous variables? Remember … as per the title of Hawking's book … the rest is man's work.

Ants figure out intrestellar kind of thing

Classic explanation!!! 😊

We ain't talkin about random variables that are polite. Lol

and yes it was usain bolt

those of you were wondering,an average elephant would weigh 2700-6000 kg depending upon the specie

"well they arre limited by the speed of light" lol sal

Had a good laugh when he said "we are not talking about polite random variable" LOL thats funny.

LMAO " We are not talking about variables that are polite." Sal said this in such a way that just made me crack me up

REALLY LOVE ❤❤ your video bro.

– 1st year university student, PHL

I feel you got a bit side tracked on this video.

Excellent video!!

The distribution of profits of a blue -chip company relates to discrete or continuous variable?

Very Nice explanation on discrete vs continuous variables

That last example enlightened me. Thanks for this vid

Basically ALL measurement quantities are continuous random variables.

This helped me a lot 😊

God bless you🙏

mass of elephant (largest) 10886.217kg ?

Don't think it is useful though

So are Likert scale points discrete or continuous? Discrete, right? But are answers to several Likert questions, when combined, for linear regression? Or logistical regression?

Can random variable have decimal value???

I honestly don't know where I'd be without you Sal !

Now the exact winning time is also a discrete random value

I really wish my lecturer were close to being this good at teaching

thank you

nice one

What is statistics

Your handwriting is beautiful!

Here is a student from Saudi.

Thanks.

The mass of a massive elephant is approximately 6000 kg 🙂

@ 9:13 Usain actually won that one too!😂😂

Thanks for the great examples! It cleared up a lot of confusion!

1985 – J Cole's birthday

Nice Video 😊😊😊😊😊😊😊😊😊👌👌👌👌👌👌👌👌👌👌👍👍👍👍👍👍👍👍👍👍👍👍👍👍👍👌👌👌👌😊😊👌👌👌👌👍👍👍

bluw whales can weigh around 190,000kgs and whale sharks about 11,800Kgs.

you are literally amazing yho

Explain in hindi

For those who don't quite understand, discrete R.V is for counting; continous R.V is for measuring.

thank u💕

Sir what you say we can't understand pls say clearly

did he said new orleans zoo where i grew up. xd. great video though thanks

Argued this with my friend today and he kept saying I was wrong when I was saying continuous is where it is like an irrational number, they can have no ending, no precise number, or infinite values within two numbers, I knew I was right

Thank you very much, it was a very clear and helpful explanation

Thank you^^

Very helpful, thanks

as usual very boring lectures

What if I had a range of values (such as the mass referred here) but to a given precision (like 2 decimal places)? Would that be discrete or random?

just a suggestion that you should have to speak a little clear and loud. In the video you pitch is high in the starting and then slowly the sound disappears

thank you so much for your youtube channel Khan Academy.

Lemony Snicket?

Best explanation.

Any instrument used to measure time will always have to be rounded or cut off some accuracy, since time is infinitely dense and cannot be measured to the exact value, so any measurements, and any units, of time that one will come across, in actual life and practice, will always be discrete, and the only difference between instruments would be accuracy and less or more discreteness on some place on a spectrum between discrete to truly continuous.

It's the same with mass. Any animal measured with any instrument will produce discrete values, so when do we treat the data recorded as discrete or continuous? Is it based on our intentions? Do I treat a set of data, such as the mass of animals, as discrete if the discrete and inaccurate values are the only thing of consequence to what I am doing, but then continuous if I am concerned with accuracy, but I have used those discrete values by virtue of the fact that my instruments are limited, but I would measure more accurately if it were possible? The data would be the exact same, but I want only the discrete values in the first situation, and I am restricted to them in the second

Much like when you talk about the 100 m sprint that rounded to the nearest 100th, you class this as discrete. What if I have the exact same set of data, but it is because my instruments are not accurate enough?

I find it odd that whether with consider data to be discrete or continuous, and follow through with using the models of the problem that warranted given either a continuous or discrete variable is based on what we intend to measure, rather than the actual data itself? In reality, every possibly continuous type of data is going to be rounded, like the sprint example, and therefore become regarded as discrete

Polite random variables

Is this science or math because I’m trying to do math and he’s doing science I don’t understand this at all

Thank you, sir.

Discrete random variables cannot be broken down into decimals or fractions.

There is no half an ant or half a person. but there can be half a second and one-fourth of a meter.

Discrete things are counted.

continuous things are measured.

😞

Adult Blue whale

Mass:

50,000 – 150,000 kg

4:12

I thought i lost hope in understanding the discrete and continuos r.v ….then i watched this video!! IT WAS SO EASY to understand thanks

Thank you for this! It helped a lot.

a good example of continuous random variable:Reading the temperature of a room throughout the day ,its continuous since the temperature does not jump from 20 degrees to 22 degrees.so its continuous process.

merci beaucoup Monsieur 🙂

10:07 is time continuous?