Okay in this video. I’m going to talk [about] finding the expected value [of] a data set that has finitely many outcomes

So my outcomes here labeled x sub 1 x sub 2 up to x sub n

And these will occur with probability p sub 1 piece of 2 up to p sub N

Respectively, and it says the expected value of your data set that’s what the x represents [basically] it’s it’s sort of out

you can think about it as being a weighted average or a

Long-Run average and all it all you have to do to compute it is

You take your outcome multiply it by its respective probability of occurence add all of those together and hey, that’s your expected value

So I’m going to do one here in conjunction [with] a game ok

so suppose your friend comes up to you and offers to play a game and

So maybe you’ll play maybe you won’t and maybe your friends not so good at statistics

and he doesn’t really he or she doesn’t really know whether

you know whether they [should] be playing the game or not, but you’ll be clever enough [to] figure it out, so

supposed to play the game it only costs one dollar and

Forgive my bad artistry so suppose you have like a little [a] little spinner, okay?

So that’s what the circle is and I’ve tried to divide it into four equal regions. So again forgive my artistry

[so] you’re going to spin the little blue spinner and whatever you know the [arrow] [is] pointing at whatever region?

It’s in you’ll get that amount of money

and for

Simplicity’s sake let’s just assume that this it will never fall on a line

You can always decide it falls into one region or the other region

Okay, so the outcomes here are you can win $0 $2 $1 $0 or $10?

Okay, and if you win the game you [know] you don’t get your initial $1 back

You just get so you pay a dollar and then your friend will pay you whatever amount is shown

Okay, so a couple things here

we need to list all of our outcomes and

the probability associated with each of those outcomes

Okay, so let’s see here. It looks like you can win

[$0] if it falls in the top left corner and also in the bottom right to me

It looks like you know just based on the area of the circle

The top left portion would be [one-fourth] of the circle

[the] bottom right portion would be another 1/4 of the circle so to me. It looks like you could win

$0 with a probability of 1/4 plus 1/4 or

1/2 so there’s a 50% chance. It’s going to fall in one of those two regions

So you’ll win $0 I can win a single dollar

so if this whole entire region represents 1/4 of the circle well if I divide that by 2

each Little region

Will have area 1/8 of the circle?

Okay, so it says the probability of me falling in the region where I would win one dollar would be 1/8

likewise the probability of me winning [$10] would have

probability 1/8 and I think the only other

Possibility would be to win $2 and again that takes up 1/4 of the circle

So the probability that I would win $2 is 1/4

Okay, so notice I [left] a little space [here] at the beginning

One of the outcomes for sure is that [you’re] going to lose [$1]

with a probability of [one]

okay, and basically what this

[represents] this just factors into the fact that well it costs

$1 to play the game

Okay, so let’s see what what the expected value of this game is

Okay, so all it says is again if we call our data set x it says we’re going to lose [$1] with 100%

Certainty we add to that okay. We’ll take zero times one half so again. I’m just multiplying

The Outcomes by their probabilities plus one times [1/8]

plus 2 times 1/4 plus 10 times [oops]

Plus 10 times 1/8

Okay, so now all that’s left to do is to basically compute the value, so I’ll get negative [one] [zero] times 1/2 is zero

Plus 1/8

It looks like I’ll get plus 2 over 4 and then

[Plus] 10 over 8

So it looks like I’m going to get common denominators here, so it looks like 8 is what we’ll use

So I’ll make that negative 8 over 8 and if I multiply top and bottom

Of my other fraction I’ll get 4 eighths, so now all I have to do is add these all up

It says you get negative 8 plus 1 which is negative 7 negative 7 plus 4 [is] negative 3 negative

3 plus 10 is

7 so we get the [value] 7 8 and

You know the important thing here is

What does this mean?

Okay, so seven eighths is the number

Point eight seven five so what it says is it says you can expect

to win

On average this [is] the important part

You can expect to win on average

eighty seven and a half cents per game

Okay, so again. This is why I say on average you know notice

The only thing that can happen is you definitely lose your dollar?

[and] then sort of the positive outcomes as you don’t either you win zero dollars one dollar two dollars or ten dollars

Okay, it’s not possible to win point eight seven five dollars per game, but again

It’s a long-run average and what it means is on the whole you’re going to win money

so if your friend offered to play this game, you would say

Absolutely, I would play this game

Suppose you played 100 times

so if you play 100 times

You could expect to win

You could expect to win

0.875

times

100 so that would simply move the decimal place twice or give you 87 50, so if you can expect to win

[0.875] dollars each time you play you could expect to win Roughly eighty seven and a half dollars if your friend

Was crazy enough to play with you for that long, [so] this is the basic notion of expected value

So it [represents] an average somehow weighted average so all right. I hope this [example] makes some sense

So you know don’t don’t offer to play this game with somebody where you’re the one charging a [dollar]?

for sure, so

Again, I think it’s a nice [little] illustration

I kind of use these game examples just to remind myself of

What expected value is I think it gives you kind of a good little intuitive idea of what’s going on so all right again

I hope this helps if you have any questions, or comments, please feel free to post them as always

Thank you. This helped me understand expected value the day before my final.

@laucherhan I think the 1 dollar you spend in each game is already factored in calculating the E(X)

The probability of me being lost is zero now thanks to you 🙂

I think ur right. the person who payed 100 can expect 87.50 in return

I was pretty sure I understood the gist of this while working on a problem but was double checking my work. Stumbled here and you clarified it. Thanks!

Never really paid attention in stat class….. exam in about a week….No problem I got patrickJMT to help me 😀

THis helps a LOT! THanks:)

lucky that I didnt listen to the professor

Patrick you're just so funny and amazing all at once. So grateful 4 ur vids 😀

No, he already factored in the loss of one dollar every game with the red -1 and 1

Well, I failed stats last year and I am doing everything – even YouTube – do pass this year. Thank goodness I clicked on your videos. Our professor should watch your videos to see how it should be explained.

Isn't the lower half of the table supposed to be a density function? In which case all the probabilities would have to add up to 1? It seems more logical to leave out the 100% chance of losing a dollar and just subtract it at the end. So the game has an E(X) of 1.875, but it costs a dollar to play so the net gain is 0.875.

Thanks for the help – these vids really do help. Question for you, how much WOULD you pay to play this game…assuming a risk:reward ratio of 1:3?

And so the day before the midterm, not only did I learn that there was a God, but that he posted youtube tutorials on statistics.

I started EV chapter today and i was lost..it helps me a lot..thanks.

Wow, you actually make statistics fun! My teacher is hopeless

i now get it!

Good job, thank you for the help !

Thanks this is alot of help!!

you sir. Have earn't yourself a new subscriber.

-.- lol, its data management, where in this video do you see derivatives and integrals?

Can you at least start writing textbooks?

helped alot thanks

Thank man

how about finding the mean??? :))

At first it seems like getting $0.875 for spending a $1 is a bad choice. Is the right way to interpret this Expected Value problem as:

"I'm spending $1 to receive an average of $1.875 per spin, thus netting $0.875?"

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Thanks a lot. I've watched your videos for pre-calc and everything. I'm taking AP stats right now and having a lot of troubles.

How do you do this if you aim to win the 10 dollars in 4 tries? Then what will your expected outcome be? I can do this basic stuff, but I just recently got hit with an intense version about shooting darts and I can't figure it out for the life of me.

You're my favorite math tutor on Youtube. I've passed my math classes thanks to you. I just wish you had more stats videos!

Thank you!!

First let me say I wish you were my math teacher! Second thanks for all your videos they are getting me through my advanced math in university! Can you help me with this:

your friend bets you $20 that he can pull 2 spades in a row from a deck of 52 cards (which contains 13 spades). What is your expected value from this bet?

a. 17.65

b. 17.76

c 18.24

d 18.57

Where did the 1/4 come from?

I find it more intuitive to subtract the dollar spent to play, into the winnings yielding …

outcome : -1 : 0 : 1 : 9

probability : 0.5 : 0.125 : 0.25 : 0.125

Patrick, can you explain the Proof for the E(X)?

Dear Patrick, thank you for this video!

I've one question . suppose you are required to pay 1$ each time you plan ( not paying one time 1$) how you describe this on that Outcome&Probability table?

i have been doing some search on this topic for a while, and this is probably the best explanation i have seen. good job

So u have to explain to us that in this example the arrow will always fall on a value and not on a line but u decide not to explain what Xn and Pn mean?

Thanks alot my teacher isn't very good so this was very helpful

Thank you! You're awesome!

I'm at the top group of math but if I want to still septa you then I have to get nothing wrong!

THANK YOU!!!!!! This was a great, easy explanation.

I have a final in 6 hours and you always save me, thank you so much!

you are terrible

HELP!

If you know that 35% of university students require vision correction (glasses or contact lenses) and assume that enrolment in classes is random,

(a) How many students would you expect to require vision correction in a class of 40?

(b) What distribution would the number of students in a class of 40 that require vision correction follow? Why?

(c) What is the probability that less than 10 students in a class of 40 require vision correction?

A winning straight ticket earns $5,000 and the winning box ticket wins $2,000 for Cash-3, what is the expected value for each type of bet if each ticket costs $1 and you either win or you lose?

Anyway you could help me out with this?

Thanks for making a statistics video that isnt the most boring thing on the planet

ok so does this mean you win $1.875 per game then? otherwise you are loosing money because it costs a dollar to play?

what about standard deviation?

I wish you were my professor !!!

Helped lots thanks

What is the random variable X in this example

what's the probability function of X?

But you said you don't win back your original dollar? So if you played 100 times and won $87.50, you'd have lost money?

perfect…

Thanks! Really helpful!

Why Expected Value can be used in statistics, people choice is not a possibility, by why when doing chi square test we involved Expected Value in it..?

a bag contains 4 red coloured beads and 6 green coloured beads. Two beads are drawn, one after the other, without replacement. Suppose X is a random variable which represent the number of red beads drawn, find E(X).

anyone can help to solve?

what if the probabilities are not based on the circle

Thank you so much!:) I'm taking liberal arts and a lot of it is expected value.This helped me!!

Very nice video. But I don't understand why -1 has to be considered. Isn't the notion of losing $1 captured by the sector having $0?

The pie example through me off, I thought since 0 was an option twice it would be 2/5 which would give you a probability of .4, and everything else a probability of .2

Beautifully explained. I will use this money example. It's effective. XD

I wish my stats teacher could explain stuff simple like you. Great vid, helped me out a lot

Thanks great video math exams tomorrow for me last second studying 😰

im confused whether we have to give 1$ on each play or only at starting

Please anyone rply

its urgent

Dear Patrick- Thanks for the video as always helpful. However, I believe that E(X) is independent of the number of times the game is played so whether you play once or 100 or 1000 times the E(X) will remain 0.875.

How probability is 1 for Outcome -1 in given timeline 3:50 ?

I really wish you had some expected value vids for advanced graduate level math like stochastic processes…those are such a pain :/

Very simple explanation to a seemingly tough concept! Thanks!!

Excellent. Very clearly explained and simple to understand.

splendid specially outcome losing dollar and probability 100 %

If you win a dollar, you just get your dollar back, so that's (0*.125) or one-eighth of the spinner. Zero times anything is zero so you can leave that off if you want.The chance that you would lose your dollar is fifty percent, or expressed as a probability is .50 since the zero takes up half the spinner (-1*.50). The 10 dollar space pays off only 9 dollars since you don't get your dollar back, and that is one-eighth of the spinner, or .125 as a probability (9

.125) The 2 dollar pays only 1 dollar since you don't get your original dollar back or (1.25)(0

.125)+(-1.50)+(9*.125)+(1*.25)=.875perty gud…

very interesting . well explained

I don't understand the last statement. You're paying $100 to play 100 times so that you can win $87.50?

Hi patric.

I have truble understanding the analysis at the end. If the player playes 100 times and the E(X) = 0.875, the player is expected to win $87.5. At the same time the the player must spend $100 to play 100 games, wouldnt that mean that the player is loosing $100 – $87.5 = $12.5? Or does it consider the 1 dollar spendt per game so the gain is actually $187.5?

Great videos btw.

Cool video. NAHT.

Hi, playing 100 times may win $87.50 on average but the guy have to pay $100 to play 100 times. Then how will this be a profit. Please reply

Nice lecture! Thanks!

I don't know what he's talking about, that circle looks fine!

Can u explain me how does this even work

there is 5 spaces yet you said 1/4 prob + another 1/4. This should be 2/5 should it not?

Onto another video..

so he'd be in loss,on average …since $0.875 is how much he'd win for every $1 spent, that a 12 cents loss on average.

cool. thanks

Can I have a question.please do answer me

Suppose that you are playing a game with single die assumed fair. In this game, you win Rs 20 if a 3

turns up. Rs 40 if a 5 turns up, lose Rs 30 if a 6 turns up. You neither win nor lose if any other faces

turn up. What is the expected sum of money you win?

thanks!

Just Awesome!!!

I don't understand why you should play the game. It costs you 1 ticket every try and on average your expected return is 0.8$. Doesnt that mean ure losing 0.2$ every game?

Hi Patrick. The table you created is not a discrete probability distribution table, correct? If not, what is it called? For the sum of the p(x) ≠ 1. thx

I got it right!!!! 🙂 thanks for sharing!!!

I don't see why this game is profitable for the ones playing ? On average you win 0.875 cents per game, but to play the game you need to give 1dollar, so on average you lose money : 0.875 – 1= -0.125cents

Why the f* did I decide to choose a career in finance -_-

I seriously wish you were my STAT prof. Your videos teach more than my prof ever could.

God bless u. The explaination is as simple as it should be

What does it indicate when the expected value is 0?

You played 100 games

One million subs, congrats!

Yo I bullshitted my performance final and got it right 😂😂😂

so if I played 100 times spending $100, would ! win $87.50 back but lose $13.50, or would i win back the $100 plus $87.50?

6:44 isn't this gambling