Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °
You are not logged in.
#26 2013-03-08 22:57:54
- anonimnystefy
- Real Member
Offline
Re: Simulations
Yes, I do.
By the way, I finally downloaded Acton's book.
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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#27 2013-03-08 23:01:10
- bobbym
- Administrator
Offline
Re: Simulations
What took you so long with the book? He has another one too.
That is good work with the histogram. I need to do a chore I will be back in about a half hour.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#28 2013-03-08 23:03:55
- anonimnystefy
- Real Member
Offline
Re: Simulations
Well, first I couldn't find a site that offers a *free* download. And then I forgot about searching.
Okay, see you then.
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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#29 2013-03-08 23:18:29
- bobbym
- Administrator
Offline
Re: Simulations
Hi;
Okay, I got it. Lets start generating random numbers from non - uniform distributions!
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#30 2013-03-08 23:20:51
- anonimnystefy
- Real Member
Offline
Re: Simulations
So, we need to transform a non-uniform into uniform ditributions, right?
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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#31 2013-03-08 23:21:46
- bobbym
- Administrator
Offline
Re: Simulations
Nope, the other way. We are going to transform a uniform into another distribution.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#32 2013-03-08 23:26:46
- anonimnystefy
- Real Member
Offline
Re: Simulations
Okay, but how?
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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#33 2013-03-08 23:36:19
- bobbym
- Administrator
Offline
Re: Simulations
We want to generate random numbers that are from the PDF f(x) = 2x from 0 to 1.
Solve the equation
for x. You get 2 solutions:
We take the positive one. Can you get maxima to do everything so far?
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#34 2013-03-08 23:52:55
- anonimnystefy
- Real Member
Offline
Re: Simulations
Yes. Should I plot a histogram for sqrt(random(1.0))?
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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#35 2013-03-09 00:05:24
- bobbym
- Administrator
Offline
Re: Simulations
Hi;
Correct! Get 10000 of them. You should get something like the picture. Notice how neatly our random numbers fit under y = 2x ( the red line ).
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#36 2013-03-09 00:11:07
- anonimnystefy
- Real Member
Offline
Re: Simulations
Yup. Got it.
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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#37 2013-03-09 00:12:39
- bobbym
- Administrator
Offline
Re: Simulations
There is only only more trick for the original problem.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#38 2013-03-09 00:16:50
- anonimnystefy
- Real Member
Offline
Re: Simulations
Which 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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#39 2013-03-09 00:17:52
- bobbym
- Administrator
Offline
Re: Simulations
It is not from 0 to 1. So you will have to do a change of variable to get it into that interval.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#40 2013-03-09 00:21:37
- anonimnystefy
- Real Member
Offline
Re: Simulations
What is not from 0 to 1?
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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#41 2013-03-09 00:23:16
- bobbym
- Administrator
Offline
Re: Simulations
Look at the PDF in post #1. It is from 1 to 2.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#42 2013-03-09 00:25:30
- anonimnystefy
- Real Member
Offline
Re: Simulations
Okay, so, what should I do?
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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#43 2013-03-09 00:28:13
- bobbym
- Administrator
Offline
Re: Simulations
Make the substitution of x = x + 1. That produces a PDF from 0 to 1. Now do everything the same. You will get a histogram like the one in post #1. The expectation will be 1 less because of the substitution.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#44 2013-03-09 00:32:05
- anonimnystefy
- Real Member
Offline
Re: Simulations
I am confused now.
Where and when do I make that substitution?
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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#45 2013-03-09 00:35:05
- bobbym
- Administrator
Offline
Re: Simulations
Now just do everything the same.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#46 2013-03-09 00:41:53
- anonimnystefy
- Real Member
Offline
Re: Simulations
I get
for the CDF.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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#47 2013-03-09 00:48:47
- bobbym
- Administrator
Offline
Re: Simulations
Hi;
Yes, that is correct. But we do not need it.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#48 2013-03-09 00:50:11
- anonimnystefy
- Real Member
Offline
Re: Simulations
What do we need?
Oh, and I get
for the inverse.
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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#49 2013-03-09 00:53:06
- bobbym
- Administrator
Offline
Re: Simulations
The integral from 0 to x, repeat post #33
The inverse is in terms of y.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#50 2013-03-09 00:57:12
- anonimnystefy
- Real Member
Offline
Re: Simulations
Well, since the PDF is 0 for x<0, the integral from 0 to x is exactly the CDF.
Yes, it is. But what range should I have for y?
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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón