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You are not logged in. #1 20130308 13:59:55
SimulationsHi;
What is the expected usage for gas for the coming week? A number of different answers are given. How can we get the answer using a CAS and simulating the process? 1) Define the PDF in mathematica as: Code:myPDF[]=ProbabilityDistribution[2(11/x^2),{x,1,2}]; 2) Run the simulation a million times. Code:data=RandomVariate[myPDF[],10^6]; Below is a histogram of data. Code:Mean[data] 1.61357 is returned. So the facility expects to use about 1613 gallons of propane this week. Last edited by bobbym (20130308 14:35:57) 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. #2 20130308 20:04:34
Re: SimulationsAnd it agrees with my answer of 32ln(2). 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 20130308 20:12:25
Re: SimulationsMore importantly were you able to duplicate the answer with your package? 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 20130308 20:14:32
Re: SimulationsI will try later. 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 20130308 20:17:50
Re: SimulationsOkay, you will find it interesting. 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 20130308 20:57:29
Re: SimulationsWhat kind of distribution would that be? 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 20130308 21:08:50
Re: SimulationsThe one given in post #1 of course! 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 20130308 21:11:16
Re: SimulationsYes, but what kind is it? Maxima needs me to specify if it is a normal, geometrical, exponential,... 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 #10 20130308 21:41:35
Re: SimulationsI am not sure how to do it, 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 “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #12 20130308 21:45:55
Re: SimulationsYes. 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 20130308 21:49:02
Re: SimulationsHi; 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 20130308 21:50:20
Re: SimulationsThat is okay. 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 20130308 22:02:23
Re: SimulationsI want to draw random numbers from the PDF y = 3x^2 from 0 to 1. Follow? 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 20130308 22:02:56
Re: SimulationsYes. 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 20130308 22:08:25
Re: SimulationsThen I take the RHS of that equation where I solved for x and integrate wrt y. 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 20130308 22:12:27
Re: SimulationsOkay. What now? 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 #19 20130308 22:13:42
Re: SimulationsI replace each y in the answer with a random variable that is uniformly distributed between 0 and 1. 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. #20 20130308 22:31:29
Re: SimulationsHm, why does it work? 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 #21 20130308 22:33:31
Re: SimulationsIt doesn't, I think I have it now though. To follow you must know how to generate random numbers between a and b in maxima. Do you follow? 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. #22 20130308 22:36:42
Re: SimulationsYes. I have the function. 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 #23 20130308 22:38:30
Re: SimulationsOkay a little theory before we go any further. If you generate 10000 random numbers between 0 and 1 what do you call that distribution? 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. #24 20130308 22:40:37
Re: SimulationsUniform. 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 #25 20130308 22:41:31
Re: SimulationsYou will need to know how to get a histogram of those 10000 points with 10 boxes. Do you know how? 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. 