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@@ -9,19 +9,15 @@ from numpy.random import exponential, poisson
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def find_relative_frequency(n_experiments, b):
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# First get the mean counts for each experiment
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- mean_counts = exponential(scale=b, size=n_experiments)
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+ a = exponential(scale=b, size=n_experiments)
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# Since this is a counting experiment, sample from a Poisson distribution with the
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# previously generated means.
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- single_counts = poisson(lam=mean_counts)
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+ x = poisson(lam=a)
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- # Generate the per-experiment bounds based on the observed single_counts
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- bound_low = single_counts - sqrt(single_counts)
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- bound_high = single_counts + sqrt(single_counts)
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-
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- # Finally, count for how many experiments the mean_count lies in the range
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- # calculated above.
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- n_pass = sum((bound_low < mean_counts) & (mean_counts < bound_high))
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+ # Finally, count for how many experiments the a lies in
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+ # the range [x-sqrt(x), x+sqrt(x)]
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+ n_pass = sum((x - sqrt(x) < a) & (a < x + sqrt(x)))
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relative_frequency = n_pass / n_experiments
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# and print the results
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@@ -30,3 +26,7 @@ def find_relative_frequency(n_experiments, b):
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find_relative_frequency(10000, 5)
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find_relative_frequency(10000, 10)
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+
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+# Example output
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+# > For b=5, 6012/10000 passed, R=60.12%
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+# > For b=10, 6372/10000 passed, R=63.72%
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