python之使用 tensorflow 概率解决掷骰子和抛硬币问题，方差是错误的

我对统计不是很精通，我正在努力学习。所以请多多包涵。我看到了this Quora 中的问题 - 基本上陈述了以下内容 -

A fair dice is rolled if the result is an odd number then a fair coin is tossed 3 times. Otherwise, if the result is even number then a fair coin will be tossed 2 times. In both cases, # of heads is counted. What's the variance of # heads obtained?

我想使用 Python 和 tf-probability 来解决它。这是我所做的-

import tensorflow as tf 
import tensorflow_probability as tfp 
import numpy as np 
tf.enable_eager_execution() 
probs = [1/6.] * 6 
 
dices = tfp.distributions.Multinomial(total_count=1000, probs=probs) 
 
n = dices.sample() 
 
HEAD = 1 
TAIL = 0 
l = list(n.numpy()) 
heads_even = [] 
heads_odd = [] 
for i, nums in enumerate(l): 
    mul_by = 3 if (i + 1) % 2 != 0 else 2 
    tosses = tfp.distributions.Bernoulli(probs=0.5) 
    coin_flip_data = tosses.sample(nums * mul_by) 
    l2 = coin_flip_data.numpy() 
    unique, counts = np.unique(l2, return_counts=True) 
    head_tails = dict(zip(unique, counts)) 
    if (i + 1) % 2 != 0: 
        heads_odd.append(head_tails[HEAD]) 
    else: 
        heads_even.append(head_tails[HEAD]) 
 
total_heads = heads_odd + heads_even 
final_nd_arr = np.array(total_heads) 
print(final_nd_arr.var()) 

但是，final_nd_arr.var() 当然与实际答案相去甚远(它是 2089.805555555556)，0.68(正如人们在 Quora 答案中提到的那样)。

我无法找出我做错了什么。我该如何纠正我的错误？

任何指针都会有所帮助。非常感谢。

------------ 编辑

为了提供更多的数据，

dices.sample() => array([169., 173., 149., 171., 175., 163.], dtype=float32) 
heads_odd => [266, 210, 259] 
heads_even => [176, 167, 145] 
total_heads => [266, 210, 259, 176, 167, 145] 

请您参考如下方法:

您正在计算错误分布的方差。我们正在寻找的方差适用于您将一遍又一遍地掷骰子的实验，每次都计算正面的数量，并计算正面数量的方差。您在您的代码中执行此操作，但您要求和所有掷骰子正面朝上的总数，然后为每个可能的骰子结果取这些总和的方差。

这将给出正确的结果。我添加了一些评论，希望能澄清它:

import tensorflow as tf 
import tensorflow_probability as tfp 
import numpy as np 
 
tf.enable_eager_execution() 
 
# Simulate the outcome of 1000 dice rolls 
probs = [1/6.] * 6 
dices = tfp.distributions.Multinomial(total_count=1000, probs=probs) 
n = dices.sample() 
l = list(n.numpy().astype(int)) 
 
L = [] 
# Loop over 6 possible dice outcomes 
for i in range(len(l)): 
    # Loop over the rolls for this dice outcome 
    for _ in range(l[i]): 
        # For each of the dice rolls, 
        # Flip a coin 2 or three times 
        num_tosses = 3 if (i + 1) % 2 != 0 else 2 
        tosses = tfp.distributions.Bernoulli(probs=0.5) 
        coin_flip_data = tosses.sample(num_tosses) 
 
        # And count the number of heads 
        num_heads = np.sum(coin_flip_data.numpy()) 
        L += [num_heads] 
 
np.var(L) 
> 0.668999