Lab 5: Simulations
Welcome to Lab 5!
We will go over
iteration
()
and
simulations
()
, as well as introduce the concept of
randomness
()
.
The data used in this lab will contain salary data and other statistics for basketball players from the 20142015
NBA season. This data was collected from the following sports analytic sites:
Basketball Reference
()
and
Spotrac
()
.
First, set up the tests and imports by running the cell below.
In [1]:
1. Nachos and Conditionals
=====================================================================
Assignment: Simulations
OK, version v1.12.5
=====================================================================
# Run this cell, but please don't change it.
# These lines import the Numpy and Datascience modules.
import
numpy
as
np
from
datascience
import
*
# These lines do some fancy plotting magic
import
matplotlib
%
matplotlib inline
import
matplotlib.pyplot
as
plt
plt.style.use(
'fivethirtyeight'
)
# Don't change this cell; just run it.
from
client.api.notebook
import
Notebook
ok
=
Notebook(
'lab05.ok'
)
In Python, the boolean data type contains only two unique values:
True
and
False
. Expressions containing
comparison operators such as
<
(less than),
>
(greater than), and
==
(equal to) evaluate to Boolean values.
A list of common comparison operators can be found below!
Run the cell below to see an example of a comparison operator in action.
In [2]:
Out[2]:
3
>
1
+
1
We can even assign the result of a comparison operation to a variable.
In [3]:
Arrays are compatible with comparison operators. The output is an array of boolean values.
In [4]:
array([False,
True,
True,
True, False, False])
Out[3]:
True
Out[4]:
result
=
10
/
2
==
5
result
make_array(
1
,
5
,
7
,
8
,
3
,

1
)
>
3
One day, when you come home after a long week, you see a hot bowl of nachos waiting on the dining table!
Let's say that whenever you take a nacho from the bowl, it will either have only
cheese
, only
salsa
,
both
cheese and salsa, or
neither
cheese nor salsa (a sad tortilla chip indeed).
Let's try and simulate taking nachos from the bowl at random using the function,
np.random.choice(...)
.
np.random.choice
np.random.choice
picks one item at random from the given array. It is equally likely to pick any of the
items. Run the cell below several times, and observe how the results change.
In [5]:
To repeat this process multiple times, pass in an int
n
as the second argument. By default,
np.random.choice
samples
with replacement
and returns an
array
of items.
Run the next cell to see an example of sampling with replacement 10 times from the
nachos
array.
'neither'
'cheese', 'both', 'neither'], dtype='<U7')
nachos
=
make_array(
'cheese'
,
'salsa'
,
'both'
,
'neither'
np.random.choice(nachos)
np.random.choice(nachos,
10
In [6]:
Question 1.
Assume we took ten nachos at random, and stored the results in an array called
ten_nachos
as
done below. Find the number of nachos with only cheese using code (do not hardcode the answer).
Out[5]:
'neither'
'cheese', 'both', 'neither'], dtype='<U7')
nachos
=
make_array(
'cheese'
,
'salsa'
,
'both'
,
'neither'
np.random.choice(nachos)
np.random.choice(nachos,
10
Out[6]:
array(['salsa', 'neither', 'cheese', 'both', 'salsa', 'cheese', 'both'
,
)