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[MUG] Problem using evalf(Int(..)) to verify density function
| [MUG] Problem using evalf(Int(..)) to verify density function |
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Author: Jay Porter
Posted: Fri, 31 Jan 2003 13:14:46 -0500
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>> From: "Jay Porter" "Jay.Porter"
The following function represents a probability density for a random
variable that can take values from zero to infinity (the RV is the
square of a gaussian RV with parameters mu and sigma):
pdf := y ->
1/4*(exp(-1/2*(y^(1/2)-mu)^2/sigma^2)+exp(-1/2*(-y^(1/2)-mu)^2/sigma^2))
/sigma*2^(1/2)/(Pi*y)^(1/2)
As a density, the integral of pdf over (0,infinity) should be 1 (when mu
and sigma are assigned numerical values).
Letting mu := 33, sigma := 1, and evaluating from 0 to infinity gives
nonsense; .8113159769e-27
Trial and error showed that with mu := 33, sigma := 1, the following
results occur:
evalf(Int(pdf,323.6564001046500000000000000000000000000000 .. infinity))
= .2581090335e-12
evalf(Int(pdf,323.6564001046500000000000000000000000000001 .. infinity))
= 1.000000000
The critical number varies with mu and sigma, but the problem persists.
As well, I've tried defining pdf as an expression and I got the same
results.
Any input would be greatly appreciated.
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