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I've seen this question posted on a soccer site, some fellow needing help. I haven't got a clue what it means. Anyone here know? "In a probability density function, what does the amplitude of the PDF represent? I know how wide it is represents its variance and its mid-point the mean, but I was wondering if the amplitude represented anything or if it was just directly related to the variance."

Question #107343. Asked by BIG_Flicker. (Jul 23 09 5:14 PM)

Rowena8482

Apparently, the amplitude is used as a physical meaning for the function, and is "a complex number whose absolute value squared represents a probability"
http://en.wikipedia.org/wiki/Probability_amplitude

 Jul 24 09, 5:16 PM
gmackematix

Well, probability density functions are concerned with continuous random variables such as the life span of a fish or a human's height. The probability of the variable falling between two values is the area between the function's graph, the x-axis and two verticals crossing the x-axis at the values in question.
http://en.wikipedia.org/wiki/Probability_density_function

Graphs of PDFs are positive with the total area under them equal to one (representing certainty that the variable has some value). They do not oscillate so do not have an amplitude but may well have a maximum value (as in the classic bell curve of normal distribution). The actual values of the PDF function itself represent the probability density and have no significance in the real world beyond the most likely values of the RV clustering around the point on the x-axis with the maximum PDF.

The "Probability amplitude" referred to by Rowena refers to quantum physics wave equations and does not relate to probability density functions.

 Jul 24 09, 7:17 PM
Baloo55th

I'll take Gm's word for that, not understanding any of it but trusting his reputation.... What concerns me is that this was originally posted on a soccer site. A soccer site? ??????

http://www.pieandbovril.com/forum/index.php?showtopic=111397

 Jul 25 09, 5:03 AM
zbeckabee

More:

A probability density function (PDF) is a type of amplitude histogram drawn with specific scaling. The horizontal axis has the units of the measured variable (g, volt, inch, etc.) This axis normally spans positive and negative values, representing the entire range of the possible instantaneous values the signal may attain.

Each (of n) horizontal PDF locations represent a small span of amplitudes, just as each point in an FFT spectrum represents the output of a narrow-band filter of resolution bandwidth. The points are equally spaced in amplitude, so that the horizontal axis has resolution and spacing of ¥ÄX = 2.X^sub full-scale^/n. A bank of counters implements the measurement; these are all cleared to zero count prior to measurement. Each time an ADC sample is measured, its amplitude is used to address one (of the n) counters, whose AX encompasses the sample's amplitude. This single counter is incremented, and attention shifts to the next signal sample. All counting is halted to end the measurement. The PDF amplitude for the ith point is computed as the counts in the ¢¯th counter divided by total of all counts in all counters and by ¥ÄX.

http://findarticles.com/p/articles/mi_qa4075/is_200903/ai_n31666913/

 Jul 25 09, 8:55 AM

 What is the definition of amplitude in a wave equation?

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