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According to my lab manual, "Theory says that radioactive decay obeys statistics for which the standard deviation of the counts per time interval is equal to the square root of the mean number of counts for that interval, for cases when the mean is a large number."

I think they mean for cases where N is a large number.

In lab, taking counts from the geiger counter, I got an average of 616.56 counts per minute with a standard deviation (computed with Excel: stdev(my column of counts) of 30.74 from 25 sets of individual 1-minute counts.

But the sqrt(616.56) = 24.83, not 30.74. Thinking that it would reach about 30.74 if I had a larger N, I set up a Monte Carlo simulation on my computer. I generated N random gauissian numbers with a mean of 616.50, and a standard deviation of 30.74. But no matter how high I make N, even 1 million, I always get an answer of about 24.8 when I square the average of my random numbers.

Additionally, Googling for "Square Root of N Law of Random Counts" turns up nothing. Did the author of my lab manual just make this up?

Here's how I modeled it with the computer

Code (Text):

Private Sub Form_Load()

totalcounts = 0

n = 1000000

For k = 1 To n

counts = Grnd(616.56, 30.74)

totalcounts = totalcounts + counts

Next k

meancounts = totalcounts / n

Label1.Caption = Sqr(meancounts)

End Sub

Function Grnd(Mean As Double, sd As Double) As Double

Dim x1 As Double, x2 As Double, w As Double, y1 As Double, y2 As Double

Do

x1 = 2 * Rnd(1) - 1

x2 = 2 * Rnd(1) - 1

w = x1 * x1 + x2 * x2

Loop Until w < 1

w = Sqr((-2 * Log(w)) / w)

y1 = x1 * w

y2 = x2 * w

Grnd = Mean + y1 * sd

End Function

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# Square Root of N Law of Random Counts

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