Get out your thinking caps... I have a math problem!

Discussion in 'Archived Threads 2001-2004' started by Steve Owen, Dec 5, 2001.

  1. Steve Owen

    Steve Owen Second Unit

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    OK, here's the situation... I have a formula with multiple variables. Each of those variables has a normal gaussian distribution with it a known mean and standard deviation. I want to calculate the mean and standard deviation of the answer.

    For example, lets say the formula looks like this (my actual formula is significantly more complex, but I figured I'd try to keep it a bit simpler)...

    X = (A^2 / B) + (C * D)

    The cheap way out is to run a "monte carlo simulation" where I feed random numbers for each of the variables. EXCEL will happily spit out random numbers that fit the mean and standard deviation profile of each variable using the following function:

    =NORMINV(RAND(),mean,sdev)

    Do that a few thousand times on each variable and input the results into the formula. Then take the resulting statistical data on the results.

    But what I want is a mathmatical way to arrive at the same answer rather than the brute force "monte carlo simulation" method. I've checked my statistics text books, websites, the works. I didn't think it would be that difficult, but apparantly it's not as trivial a task as I thought. If anyone has a way to get there, I'm interested in hearing it...

    Thanks!

    -Steve
     
  2. Howard Williams

    Howard Williams Supporting Actor

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    All I know is that X is always equal to one, zero, or minus 1.
     
  3. Scott Barnhart

    Scott Barnhart Stunt Coordinator

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    Steve,
    This question is tailor-made for USENET - sci.math. Have you tried there?
    Unfortunately, I have forgotten almost all the math I ever learned. I guess most people really *don't* need it day-to-day! [​IMG]
     
  4. Rob_J

    Rob_J Stunt Coordinator

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    It's time to bring out the patented "I don't have a clue, but I must fill this space on the exam" answer: X -7
    True, it is like Cliff Claven's infamous Jeopardy answer of "who are three men that have not been in my kitchen", but logically, it is still correct (unless by some stroke of luck it is equal to -7, in which case, the gods are against you win or lose [​IMG] )
     
  5. Adil M

    Adil M Supporting Actor

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    I'll take a guess from HS stats 4 yrs ago. Assume A,B,C,D can be any number. The Standard deviationis not affected by adding C*D, lots of swiss cheese guesses here. Therefore, SD should come from A^2/B. A,B,C and D should have the same means based on assumption. So the mean is A mean (A mean + 1). [​IMG]
    Ok, this allsounds like crap to me, but here you go. It's been many yrs and I don't remember gaussian.
     
  6. Steve Owen

    Steve Owen Second Unit

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    Adil, I believe you're absolutely correct about the means. Assuming true gaussian distribution the mean of X will indeed be the equation with the means of all of the other variables plugged in.
    Still no clue about the standard deviation though... [​IMG]
    -Steve
     

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