How does np.mean() give us the probability?

Frequently Asked Questions Python FAQ
1

Question

In the context of this exercise, how does np.mean() give us the probability?

Answer

The np.mean() function is generally used to get the average of all values in a dataset. We can apply this function with a logical statement to get the percent of values that satisfy the logical statement.

In the exercise example, we have np.mean(a==4). First, this will evaluate the conditional, a==4, which will return a list of True and False values. Then it will run np.mean() on that list of True and False values. When running np.mean() on a list of True and False values, True = 1, False = 0 during the calculation.

Because True values count as 1, this is like counting how many elements satisfy the logical statement, and the calculation is essentially:

(Number elements satisfying condition) / (Number total elements)

Example

# a = [4, 3, 1, ..., 4]
np.mean(a==4)
=
np.mean([True, False, False, ..., True])

# In Numpy functions, 
# True  counts as 1
# False counts as 0

# This is then equivalent to calculating
np.mean([1, 0, 0, ..., 1])

# Example:
# There are 10000 total elements
# 5000 elements equal to 4
np.mean(a==4)
= 
5000 / 10000 = 0.5 or 50% probability
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2

what is the exact mathematics behind np.random.binomial function?
i understood the part it has given some particular result. I am curious to know how exactly python works in background.

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3

In this exercise - Why does ““print(no_emails)”” and ““print(b_test_emails)”” give 0.0 as results in the terminal?

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4

My guess is that there’s simply no chance any of these combinations would be possible

5

Regarding no_emails, it is due to the very small probability that emails contains at least one 0. If the probability that a recipient of one email open it is 0.05, then the probability of sending 500 emails and being opened by nobody is (1 - 0.05) ** 500. Therefore, the probability that 0 will appear even once in 10000 trials is 1 - (1 - (1 - 0.05) ** 500) ** 10000. If you calculate this, it will be about 0.000000073.

zero_out_of_500 = (1 - 0.05) ** 500
p = 1 - (1 - zero_out_of_500) ** 10000
print(p)  # 7.2745140578e-08

This is the probability of 7.3 out of 100,000,000 clicks on ‘Run’.

Regarding b_test_emails, isn’t it around 0.002 to 0.003?

6

Hello there,

Could someone tell me how to find the probability of a point in an interval, like this?
prob_more68 = np.mean(Height_girls>=68)
prob_less70 = np.mean(Height_girls<=70)

Numpy does not allow me to include an & and write it in one line, like this:

prob = np.mean(Height_girls>=68 & Height_girls<=70)

Thanks,
K

7 
prob = np.mean((Height_girls>=68) & (Height_girls<=70))
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