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#1 2012-03-22 12:15:21

TARAJS
Member
Registered: 2011-12-01
Posts: 19

Another random problem

a point is randomly selected with a rectangle whose vertices are (0,0), (2,0), (2,3) and (0,3). What is the probability that the x-coordinate of the point is less than the y-coordinate?

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#2 2012-03-22 12:20:28

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,391

Re: Another random problem

I think it is 1/3


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#3 2012-03-22 12:34:54

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,574

Re: Another random problem

Hi;



In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#4 2012-03-22 12:42:40

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,391

Re: Another random problem

Hi bobbym

how did you get that?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#5 2012-03-22 12:47:15

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,574

Re: Another random problem

x ∈ [0,2], y ∈ [0,3] both are uniform distributions. There are 3 y's for every 2 x's.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#6 2012-03-22 12:56:12

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,391

Re: Another random problem

Hi bobbym

i think i switched  x and y coordinates.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#7 2012-03-22 13:03:16

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,574

Re: Another random problem

Hi;

Or the answer is the area enclosed by the rectangle on top and the line y = x.

View Image: area.gif

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#8 2012-03-22 13:14:24

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,391

Re: Another random problem

Hi bobbym

yes that's how i did it,i just flipped the rectangle around the y=x line.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#9 2012-03-22 13:17:17

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,574

Re: Another random problem

Hi anonimnystefy;

It is late and time for you to rest. I will see you tomorrow.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#10 2012-03-22 13:19:02

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,391

Re: Another random problem

Noooooooooooo...


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#11 2012-03-22 13:20:24

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,574

Re: Another random problem

Is it not 2:20 AM?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#12 2012-03-22 13:21:09

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,391

Re: Another random problem

Yes it is.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#13 2012-03-22 13:26:07

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,574

Re: Another random problem

Yawning, sleepy eyelids, a general buildup of toxins and a lowering of body temperature all signalling the need for sleep...


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#14 2012-03-22 13:28:43

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,391

Re: Another random problem

And yet math is awaiting.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#15 2012-03-22 13:29:41

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,574

Re: Another random problem

Let the problems of the day be sufficient for the day.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#16 2012-03-22 13:31:47

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,391

Re: Another random problem

Don't understand.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#17 2012-03-22 13:34:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,574

Re: Another random problem

Math will wait.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#18 2012-12-13 13:21:08

cooljackiec
Member
Registered: 2012-12-13
Posts: 160

Re: Another random problem

actually, bobbym
The point (x,y) satisfies x<y if and only if it belongs to the shaded triangle bounded by the lines x=y,y=2 , and , x=0 the area of which is 2. The rectangle has area 6, so the probability in question is 1/3


I see you have graph paper.
You must be plotting something
lol

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#19 2012-12-13 13:38:28

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,391

Re: Another random problem

Hi cooljackiec

Bobbym's answer is correct. Take a closer look and try plotting a few values fir (x,y) to see which area the points will belong.

And, welcome to the forum! smile


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#20 2012-12-13 16:20:29

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,574

Re: Another random problem

Hi cooljackiec;

The area above the triangle that the line y = x makes is twice as large as the area below the triangle. y is a 2 to 1 favorite. There is only one probability that is twice its complement. That is 2 / 3. The probability the P(y > x ) = 2 / 3 so P(x < y ) = 2 / 3.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

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