Python数学小实验（2）——观察几种典型分布

1、观察平均分布rand，正态分布randn

import numpy as np import matplotlib.pyplot as plt #from torch import random y2 = np.random.randn(10000) y1 = np.random.rand(10000) f,(uniform,normal) =plt.subplots(ncols=2) uniform.hist(y1,bins=100) uniform.set_title('rand') normal.hist(y2,bins=100) normal.set_title('randn') plt.show() ''' def hist( x, bins=None, range=None, density=None, weights=None, cumulative=False, bottom=None, histtype='bar', align='mid', orientation='vertical', rwidth=None, log=False, color=None, label=None, stacked=False, normed=None, *, data=None, **kwargs) '''

2、观察指数分布

问题描述：每分钟内，某时间发生的概率为0.6，过了1000000分钟，求发生的时间间隔的概率分布，求发生时间间隔大于20分钟的概率

import numpy as np import matplotlib.pyplot as plt import matplotlib.mlab as mlab from collections import Counter time_stop = [] count = 0 for i in range(1,1000000): if (np.random.rand()) >0.6: count +=1 if count== 1: time_start = i else: time_stop.append(i-time_start) time_start = i print(np.mean(time_stop)) #输出均值（期望） print(np.var(time_stop)) #输出方差 print(np.max(time_stop)) #输出最大值 print(Counter(time_stop)) #输出频数统计 plt.hist(time_stop,bins=np.max(time_stop),cumulative=False) plt.show()

输出：

2.500974132346946 3.7563502939289948 26 Counter({1: 160223, 2: 95462, 3: 57655, 4: 34600, 5: 20799, 6: 12447, 7: 7325, 8: 4520, 9: 2756, 10: 1581, 11: 1028, 12: 590, 13: 352, 14: 199, 15: 133, 16: 66, 17: 41, 18: 29, 19: 19, 20: 9, 21: 5, 22: 2, 23: 1, 26: 1})

不解之处： 指数分布的期望和方差为什么会不相等？

未完待续…