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#1 2012-03-23 11:15:21

TARAJS
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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?

#2 2012-03-23 11:20:28

anonimnystefy
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Re: Another random problem

I think it is 1/3


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#3 2012-03-23 11:34:54

bobbym
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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.

#4 2012-03-23 11:42:40

anonimnystefy
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Re: Another random problem

Hi bobbym

how did you get that?


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#5 2012-03-23 11:47:15

bobbym
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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.

#6 2012-03-23 11:56:12

anonimnystefy
Real Member

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Re: Another random problem

Hi bobbym

i think i switched  x and y coordinates.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#7 2012-03-23 12:03:16

bobbym
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Re: Another random problem

Hi;

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


Uploaded Images
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.

#8 2012-03-23 12:14:24

anonimnystefy
Real Member

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Re: Another random problem

Hi bobbym

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


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#9 2012-03-23 12:17:17

bobbym
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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.

#10 2012-03-23 12:19:02

anonimnystefy
Real Member

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Re: Another random problem

Noooooooooooo...


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#11 2012-03-23 12:20:24

bobbym
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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.

#12 2012-03-23 12:21:09

anonimnystefy
Real Member

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Re: Another random problem

Yes it is.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#13 2012-03-23 12:26:07

bobbym
Administrator

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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.

#14 2012-03-23 12:28:43

anonimnystefy
Real Member

Offline

Re: Another random problem

And yet math is awaiting.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#15 2012-03-23 12:29:41

bobbym
Administrator

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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.

#16 2012-03-23 12:31:47

anonimnystefy
Real Member

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Re: Another random problem

Don't understand.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#17 2012-03-23 12:34:13

bobbym
Administrator

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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.

#18 2012-12-14 12:21:08

cooljackiec
Full Member

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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

#19 2012-12-14 12:38:28

anonimnystefy
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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


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#20 2012-12-14 15:20:29

bobbym
Administrator

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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.

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