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?