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最新推荐文章于 2024-10-16 22:13:23 发布

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最新推荐文章于 2024-10-16 22:13:23 发布

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本文介绍如何利用Python编程实现硬币翻转概率的模拟实验，并通过统计数据方差来验证实验结果的准确性。

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<pre name="code" class="python">#quote from MIT 'introduction to computation and programming using python, Revised'
import random
import pylab

def stdDev(X):
    mean = sum(X)/len(X)
    tot = 0.0
    for x in X:
        tot += (x-mean)**2
    return (tot/len(X))**0.5
    
def flipSim(flipsPerTrial, numTrials):
    fracHeads = []
    for n in range(numTrials):
        heads = 0
        for f in range(flipsPerTrial):
            if random.random() < 0.5:
                heads += 1
        fracHeads.append(heads/float(flipsPerTrial))
    mean = sum(fracHeads)/len(fracHeads)
    sd = stdDev(fracHeads)
    return (fracHeads, mean, sd)
    
def showErrorBars(minExp, maxExp, numTrials):
    """Assumes minExp and maxExp positive ints; minExp < maxExp
         numTrials a positive integer
       Plots mean fraction of heads with error bars"""
    means, sds = [], []
    xVals = []
    for exp in range(minExp, maxExp + 1):
        xVals.append(2**exp)
        fracHeads, mean, sd = flipSim(2**exp, numTrials)
        means.append(mean)
        sds.append(sd)
    pylab.errorbar(xVals, means, yerr=2*pylab.array(sds))
    pylab.semilogx()
    pylab.title('Mean Fraction of Heads (' + str(numTrials) + ' trials)')
    pylab.xlabel('Number of flips per trial')
    pylab.ylabel('Fraction of heads & 95% confidence')

showErrorBars(3, 10, 100)
pylab.show()