Learn

We can use the binom.cdf() method from the scipy.stats library to calculate the cumulative distribution function. This method takes 3 values:

• x: the value of interest, looking for the probability of this value or less
• n: the sample size
• p: the probability of success

Calculating the probability of observing 6 or fewer heads from 10 fair coin flips (0 to 6 heads) mathematically looks like the following:

$P(6\; or\; fewer\; heads) = P(0\; to\; 6\; heads)$

In python, we use the following code:

import scipy.stats as stats

print(stats.binom.cdf(6, 10, 0.5))

Output:

0.828125

Calculating the probability of observing between 4 and 8 heads from 10 fair coin flips can be thought of as taking the difference of the value of the cumulative distribution function at 8 from the cumulative distribution function at 3:

$P(4\;to\;8\;Heads) = P(0\;to\;8\;Heads) - P(0\;to\;3\;Heads)$

In python, we use the following code:

import scipy.stats as stats

print(stats.binom.cdf(8, 10, 0.5) - stats.binom.cdf(3, 10, 0.5))

Output:

# 0.81738

To calculate the probability of observing more than 6 heads from 10 fair coin flips we subtract the value of the cumulative distribution function at 6 from 1. Mathematically, this looks like the following:

$P(more\; than\; 6\; heads) = 1 - P(6\; or\; fewer\; heads)$

Note that “more than 6 heads” does not include 6. In python, we would calculate this probability using the following code:

import scipy.stats as stats
print(1 - stats.binom.cdf(6, 10, 0.5))

Output:

# 0.171875

### Instructions

1.

Uncomment and assign the variable prob_1 to the probability of observing 3 or fewer heads from 10 fair coin flips using the cumulative distribution function. Then print prob_1.

Use the binom.cdf() method from the scipy.stats library.

2.

Uncomment and run the given code for the probability mass function below the following comment:

# compare to pmf code

See how the calculation using the CDF is simpler?

3.

Uncomment prob_2 and assign the variable to be the probability of observing more than 5 heads from 10 fair coin flips. Then print prob_2.

Use the binom.cdf() method from the scipy.stats library.

4.

Assign the object prob_3 the probability of observing between 2 and 5 heads from 10 fair coin flips. Then print prob_3

5.

Uncomment and run the code for the probability mass function at the bottom of script.py. See how this calculation is simpler?