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| Re: Canarsie CBTC (100573) | |||
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Re: Canarsie CBTC |
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Posted by AlM on Sun Jun 19 06:43:34 2005, in response to Re: Canarsie CBTC, posted by Stephen Bauman on Sat Jun 18 12:15:56 2005. Hint, the magnitude of the error is independent of the velocity travelled. For simplification, you may assume that the time measurement is completely accurate.You are asking a fiendishly difficult question here. Let me state it as a probability problem. X is a vector-valued random variable with expected value (0,0,0). Let D(X) be the random variable = |X-(0,0,0)|. We are given that D(X) has a normal distribution, an expected value of 0, and variance 15x15=225. Y is a vector-valued random variable with expected value (D1,0,0). Let D1(Y) be the random variable = |Y-(D1,0,0)|. D1(Y) has a normal distribution, an expected value of 0, and variance 15x15=225. X and Y are independent. What is the standard deviation (i.e., square root of the variance) of the random variable |X-Y|? If this were all in one diminesion, you could assume that the variance of the difference of two independent normally distrbuted random variables is the sum of the variances, and the standard deviation would be 15 x SQRT(2). But it's not all in one dimension, which makes the problem very difficult. I have taught basic college level probability but don't even want to think about the integrals you'd have to do to calculate that answer. |
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