Mean value!!!

For the discussion of math. Duh.

Moderators: gmalivuk, Moderators General, Prelates

evinda
Posts: 32
Joined: Fri May 03, 2013 10:16 pm UTC

Mean value!!!

Postby evinda » Fri May 03, 2013 10:51 pm UTC

Hi!!!!I hope you can help me at the following exercise:

Consider a gamble,with the same possibility to win or to lose.If we win,we double our property,but if we lose we halve our property.Let's consider that we begin with an amount c.Which will be the mean value of our property,if we play n times(independent repetitions of the game)???

Thanks in advance!!!

User avatar
gmalivuk
GNU Terry Pratchett
Posts: 26834
Joined: Wed Feb 28, 2007 6:02 pm UTC
Location: Here and There
Contact:

Re: Mean value!!!

Postby gmalivuk » Sun May 05, 2013 8:11 pm UTC

What do you already know about means? What have you done already? Where are you getting stuck?

We are not here to do your homework for you.
Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.
---
If this post has math that doesn't work for you, use TeX the World for Firefox or Chrome

(he/him/his)

User avatar
Qaanol
The Cheshirest Catamount
Posts: 3069
Joined: Sat May 09, 2009 11:55 pm UTC

Re: Mean value

Postby Qaanol » Sun May 05, 2013 10:59 pm UTC

Can you figure out the answer for the special case n=1?
wee free kings

User avatar
Lenoxus
Posts: 120
Joined: Thu Jan 06, 2011 11:14 pm UTC

Re: Mean value!!!

Postby Lenoxus » Sun May 05, 2013 11:24 pm UTC

I can't parse this unless "mean value" is to be interpreted as "expected value". At the end of the trials you will still only have one value, so it doesn't make sense to find the mean. One could find the mean of possible values, but I don't think that's a way of solving this (?).

Anyway, I hope the following advice won't count as helping too much: One of the fun things about certain probability questions (and many other math problems) is that if you're totally stuck you can try it out yourself! Play with pennies and a twenty-sided die (or, ha, another coin), pick a number that you have to roll better than to win, and see what happens after a bajillion trials. Then see if you can explain it with math. Of course, you can't just assume that your results are what "will" happen, since this is randomness after all. That's why larger numbers of trials help. (If you know how to program it on a computer, then try that!)

Edit: I misread the question as asking for a generalization where the probability of victory is another variable along with c and n.

evinda
Posts: 32
Joined: Fri May 03, 2013 10:16 pm UTC

Re: Mean value!!!

Postby evinda » Mon May 06, 2013 11:13 am UTC

I write you what I have done until now:
n=1: E=(2c+c/2)/2=5c/4=51c/22*1
n=2: E=(4c+2c+c/4)/4=25c/16=52c/22*2
n=3: E=(14c+3c/2+c/8)/8=125c/64=53c/22*3
etc.
So, playing the game n times, the expected value is E=5nc/22*n=(5/4)nc.
Is this right??? :? :?:

User avatar
jestingrabbit
Factoids are just Datas that haven't grown up yet
Posts: 5967
Joined: Tue Nov 28, 2006 9:50 pm UTC
Location: Sydney

Re: Mean value!!!

Postby jestingrabbit » Mon May 06, 2013 1:27 pm UTC

evinda wrote:I write you what I have done until now:
n=1: E=(2c+c/2)/2=5c/4=51c/22*1
n=2: E=(4c+2c+c/4)/4=25c/16=52c/22*2
n=3: E=(14c+3c/2+c/8)/8=125c/64=53c/22*3
etc.
So, playing the game n times, the expected value is E=5nc/22*n=(5/4)nc.
Is this right??? :? :?:


It seems right to me. Although, you could prove your result with a bit of work, rather than just noticing it.
ameretrifle wrote:Magic space feudalism is therefore a viable idea.

evinda
Posts: 32
Joined: Fri May 03, 2013 10:16 pm UTC

Re: Mean value!!!

Postby evinda » Mon May 06, 2013 5:11 pm UTC

Ok,I while make a try...Thank you very much!!! :)

User avatar
Adam H
Posts: 1267
Joined: Thu Jun 16, 2011 6:36 pm UTC

Re: Mean value!!!

Postby Adam H » Mon May 06, 2013 7:06 pm UTC

Lenoxus wrote:I can't parse this unless "mean value" is to be interpreted as "expected value". At the end of the trials you will still only have one value, so it doesn't make sense to find the mean. One could find the mean of possible values, but I don't think that's a way of solving this (?).
Isn't that the common way of thinking about EV? The average result of infinite trials?

I think I actually prefer the term "mean value" because the MEDIAN is usually the value that you would expect. In this case it's 1 (for all n?), I think (Or maybe not?). And in a round of standard russian roulette, the expected value is "live" (compared to the Expected Value, which is a meaningless "one sixth dead").

Please correct me, I have no idea what I'm talking about.
-Adam

User avatar
ConMan
Shepherd's Pie?
Posts: 1691
Joined: Tue Jan 01, 2008 11:56 am UTC
Location: Beacon Alpha

Re: Mean value!!!

Postby ConMan » Mon May 06, 2013 11:39 pm UTC

evinda wrote:I write you what I have done until now:
n=1: E=(2c+c/2)/2=5c/4=51c/22*1
n=2: E=(4c+2c+c/4)/4=25c/16=52c/22*2
n=3: E=(14c+3c/2+c/8)/8=125c/64=53c/22*3
etc.
So, playing the game n times, the expected value is E=5nc/22*n=(5/4)nc.
Is this right??? :? :?:

So, since you've got this far, do you want to try proving the expected value you've found? It looks like a problem that opens itself up quite nicely to induction (although maybe not).
pollywog wrote:
Wikihow wrote:* Smile a lot! Give a gay girl a knowing "Hey, I'm a lesbian too!" smile.
I want to learn this smile, perfect it, and then go around smiling at lesbians and freaking them out.

User avatar
dudiobugtron
Posts: 1098
Joined: Mon Jul 30, 2012 9:14 am UTC
Location: The Outlier

Re: Mean value!!!

Postby dudiobugtron » Tue May 07, 2013 1:06 am UTC

Adam H wrote:I think I actually prefer the term "mean value" because the MEDIAN is usually the value that you would expect. In this case it's 1 (for all n?), I think (Or maybe not?). And in a round of standard russian roulette, the expected value is "live" (compared to the Expected Value, which is a meaningless "one sixth dead").

You really shouldn't 'expect' to live if you're playing a game of Russian Roulette. Not from a maths point of view, but just a common sense one.

Spoiler:
Man Dies Unexpectedly while playing Russian Roulette

A man was found dead Yesterday, with an empty gun in his hand. Police haven't released the full details yet, but are referring to the man as "Adam H".

Witnesses say that he was playing Russian Roulette, but police are doubtful. "You just don't expect this sort of thing to happen." Says Constable O. Blivious, the first reporting officer on the scene. "In a game of Russian Roulette, there are 5 empty chambers, and only 1 loaded chamber - so you'd expect them to live."

Police are not ruling out foul play, such as someone tampering with the victim's gun before the game.


"One sixth dead" does have some sensible meaning though - other than just the "Princess Bride"-esque meaning that you are getting from it.
I like to interpret the "one sixth dead" as meaning that you should expect to die one sixth of the time.
Image

elasto
Posts: 3778
Joined: Mon May 10, 2010 1:53 am UTC

Re: Mean value!!!

Postby elasto » Tue May 07, 2013 6:49 am UTC

To me 'expected result' implies median and 'expected value' implies mean, if I'm trying to parse layman's terms into mathematical ones.

But, in any case, 'one sixth dead' seems to be invoking common parlance in a nonsensical fashion. I'd interpret that in the same fashion as calling someone 'half dead' - ie. left for dead or nearly dead. If someone means it in a mathematical sense and not a layman sense, they should use the well-defined mathematical terms.

User avatar
Adam H
Posts: 1267
Joined: Thu Jun 16, 2011 6:36 pm UTC

Re: Mean value!!!

Postby Adam H » Tue May 07, 2013 3:10 pm UTC

OK, russian roulette was a bad example because death is not a number (and it's extreme!).

If you have a 90% chance of getting a value of 0, and a 10% chance of getting a value of 10, what value would you expect to get? Definitely not 1.

Phrases mean whatever people think they mean, so I'm not saying we should stop using the phrase Expected Value. It gets the point across fine. But if whoever is in charge of math terminology wanted to change it to Mean Value, they'd have my vote of approval.
-Adam

User avatar
firechicago
Posts: 621
Joined: Mon Jan 11, 2010 12:27 pm UTC
Location: One time, I put a snowglobe in the microwave and pushed "Hot Dog"

Re: Mean value!!!

Postby firechicago » Wed May 08, 2013 12:08 pm UTC

The problem with that is that mean value already has a well defined meaning in mathematics.


Return to “Mathematics”

Who is online

Users browsing this forum: No registered users and 9 guests