How to calculate probability of a binary function in Python?

问题

Let us consider the following function:

$f(x)=\begin{cases} 0,&  \Pr(f(x)=0)=x \\  
 1,&  \Pr(f(x)=1)=1-x\end{cases}$,

where $0< x< 1$

Trial:
I have tried with the following code but I,m not sure whether it is correct or not. The codes are here:

import random
def f(x):
    b=random.randint(0,1)
    return b

x=0.3
count0=0
count1=0
for i in range(1000):
    if f(x)==0:
        count0=count0+1
    else:
        count1=count1+1
print 'pr(f(x)=0)=', count0*1.0/1000
print 'pr(f(x)=1)=', count1*1.0/1000   

Does my code give the correct calculation? Please help?

回答1:

If you mean to say "0 with the probability of x, and 1 with the probability of 1 - x", random.random returns a random number from [0, 1), so you just check if x is greater than that number:

import random

def f(x):
    return x >= random.random()

Currently, your function returns 0 and 1 with a 50/50 chance.

回答2:

Yes, your code does the correct solution (based on the binomial distribution you've created calling N times f(x) ).

However, the probability of selecting 0 or 1 randomly from (0, 1) is 50/50, but, as you surely have noticed already, you're computing the probability for a given sample (Ex. [1, 1, 1, 1, 0]), not for the whole universe of calling infinite times f(x).

See: Binomial distribution.

You could write a more readable code if you store the results of the function in a list like this:

intents = []
num_intents = 1000

for i in range(num_intents):
    intent.append(f(x))

Then:

print('pr(f(x)=0)={}'.format(intents.count(0)/num_intents)
print('pr(f(x)=1)={}'.format(intents.count(1)/num_intents)

I also recommend you to explore numpy and binomial distributions, numpy.random.binamial

来源：https://stackoverflow.com/questions/44571472/how-to-calculate-probability-of-a-binary-function-in-python