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#51 2016-09-25 15:52:03

mr.wong
Member
Registered: 2015-12-01
Posts: 252

Re: Probability of meeting

Hi  bobbym ,

I  mean  the  x-axis  being  the  waiting  time  while  the  y-axis 
showing  the  corresponding  probability  and  expectation .

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#52 2016-09-25 16:05:12

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Probability of meeting

That would mean you could only have two parameters?! The waiting time for both would have to be the same?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#53 2016-09-25 16:46:22

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Probability of meeting

Is it not arrival time of boy/girl on x axis? Or Is it waiting time (20 minutes or less)?


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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#54 2016-09-26 15:19:57

mr.wong
Member
Registered: 2015-12-01
Posts: 252

Re: Probability of meeting

Hi  bobbym  and  thickhead ,

The  waiting  time ( willing )  for  both  will  be  the  same . The 
probability  and  expectation  can  be  shown  in  y-axis  at  the 
same  time .
Since  the  x-axis  will  show  various  values  of  waiting  time , 
i.e.  10 , 20 , 30 mins.  and  up  to  60  mins. thus  it  should  not
be  the  arrival  time . 

( I  don't  mean  the  case  of  waiting  time  of  20  mins.  only 
with  a  graph  showing  the  corresponding  cumulative  probability 
and   expectation   in  various  periods. )

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#55 2016-09-26 16:06:24

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Probability of meeting

Hi;

So, in order to graph it all one needs is a general formula for the expectation and the probability. t will be the independent variable.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#56 2016-09-26 22:29:53

mr.wong
Member
Registered: 2015-12-01
Posts: 252

Re: Probability of meeting

Hi  bobbym ,

The  formula  for  probability  will  be  1 -{ (60- t)^2 / 60^2 }   where 
t  denotes  the  promised  maximum  waiting  time  in  minutes .
But  the  formula  for  expectation  will  be  much  more  complicated .

Last edited by mr.wong (2016-09-26 22:54:36)

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#57 2016-09-26 22:38:31

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Probability of meeting

If no one else can get it I will work on it tomorrow, I am exhausted from taking a long biking trip and having to return in the night through the forest. Much stress, much fear and much adrenalin seems to have drained the energy right out of me.

One thing still puzzles me, since I was interpreting the overlaps wrong I was getting the expectation wrong. How was I getting the probability right?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#58 2016-09-26 23:34:35

mr.wong
Member
Registered: 2015-12-01
Posts: 252

Re: Probability of meeting

Hi  bobbym ,

Take  a  good  rest  before  you  do  anything ! 

The  probability  only  concerns  the  plain ( 2-dimensional) 
diagrams in  which  the  corresponding  area  we  get  are  the  same .
While  for  expectation  we  need  a  3-dimensional  diagram  with 
the  height  showing  the  waiting  time  to  get  the  total  volume 
where  we  had   divergent  opinions .

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#59 2016-09-27 03:16:22

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Probability of meeting

Hi;

Your formula for the probability checks out.

This is what I am getting for the expectation

tNRaLOz.png

where the horizontal axis is the waiting time and the vertical is the expected time to wait. But it was done while I am half asleep and needs some checking.

The formula that produces this graph is the piecewise function:

Surprisingly this says that the expected waiting time is 10 after t >= 30.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#60 2016-09-28 19:46:07

mr.wong
Member
Registered: 2015-12-01
Posts: 252

Re: Probability of meeting

Hi  bobbym ,

I  am  also  surprised  that  for  t >= 30   the  expectation  is  fixed  to 
be  10  mins.  Does  this  means  that  if  the  promised  waiting  time 
reaches  1/2  of  the  whole  time  then  the  expectation  will  be  fixed 
to  be  1/6 ?

While  for  t < 30  I  got  the  coefficient  of  t^2  to  be  - 150  instead 
of  your  4/3 * - 90  =  - 120 .  But  I  am  not  sure  that  I  am  correct .

How  about  the  graph  of  probability ?

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#61 2016-09-28 19:53:41

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Probability of meeting

To get the graph of the probability we only have to graph the formula you gave.

NlTmPFX.png


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#62 2016-09-28 20:37:07

mr.wong
Member
Registered: 2015-12-01
Posts: 252

Re: Probability of meeting

Thanks  bobbym   ,

Can  the  2  graphs  combined  into  1 ?

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#63 2016-09-28 20:46:56

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Probability of meeting

I can overlay them, that is about all I know of. This is a 2D space and our options are limited. Is that okay?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#64 2016-09-28 21:52:52

mr.wong
Member
Registered: 2015-12-01
Posts: 252

Re: Probability of meeting

Hi  bobbym ,

I  mean  the  scale  of  probability  moved  to  the  right  side 
thus  the  2  curves  can  exist  in  the  same   graph .

( I  have  checked  again  that  your  expression  for  t < 30  is  correct ! )

Last edited by mr.wong (2016-09-28 22:59:37)

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#65 2016-09-29 03:13:52

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Probability of meeting

I  mean  the  scale  of  probability  moved  to  the  right  side
thus  the  2  curves  can  exist  in  the  same   graph .

Oooh, I have never done that before in my software. I will have to read up on how to do it first.

( I  have  checked  again  that  your  expression  for  t < 30  is  correct ! )

Of course it is correct. Could my puny human bumpkin brain do that? Mathematica did that. Wiser than the Oracle at Delphi, it is...

Here is what I think you want, let me know if it is not:

nEUh0DM.gif


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#66 2016-09-29 15:20:27

mr.wong
Member
Registered: 2015-12-01
Posts: 252

Re: Probability of meeting

Hi  bobbym ,

I  don't  mean  a  pair  of  graphs ! 
I  mean  the  scale  of  probability  ( 0.2 , 0.4 , ...1.0 ) moved  to  the 
right  side  of  the  graph  of  expectation  , thus  the  2  curves 
( preferred  with  different  colours )  exist  simultaneously  in  one  graph .

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#67 2016-09-29 15:54:47

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Probability of meeting

You mean an overlay?  The scaling of the vertical axis is very different but you want them to be the same size and one on top of the other?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#68 2016-09-30 15:39:26

mr.wong
Member
Registered: 2015-12-01
Posts: 252

Re: Probability of meeting

Hi  bobbym ,

I  don't  mean  an  overlay . I  think  the  2  curves  can  match  well  with 
the  scaling  of  expectation  from  0  to  10  at  the  left  margin ,  while 
the  scaling  of  probability  from  0  to  1  at  the  right  margin ,  both 
with  the  same  height .
Many  charts  we  have  seen  nowadays  are  with  such  design .

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#69 2016-10-04 15:57:25

mr.wong
Member
Registered: 2015-12-01
Posts: 252

Re: Probability of meeting

From  the  graphs  we  can  see  that  if  both  the  boy  and  the  girl 
are  patient  to  an  average  waiting  time  of  not  less  than  30  mins. ,
then  they  should  keep  waiting  after  30  mins.  in  order  to  increase 
the  probability  of  meeting  without  increasing  the  actual  average 
waiting  time .

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#70 2016-10-05 00:07:47

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Probability of meeting

Hi;

Many  charts  we  have  seen  nowadays  are  with  such  design .

Can you give me a link to one?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#71 2016-10-05 15:22:32

mr.wong
Member
Registered: 2015-12-01
Posts: 252

Re: Probability of meeting

Hi  bobbym ,

I  have  found  one , but  not  about  mathematics .

http://ourhkfoundation.org.hk/sites/def … H_Land.pdf

( Figure 11 .  Figure 12 (b) . and  Figure 13 )

I  am  sorry  that  I  don't  know  how  to  make  a  link .

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#72 2016-10-05 16:40:41

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Probability of meeting

Hi;

I fixed the link for you, let me work on it for awhile, I might get lucky.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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