Question 1
Assign
coin_model_probabilities
to a two-item array containing the chance of
heads as the first element and the chance of tails as the second element under Gary’s model. Make
sure your values are between 0 and 1.

15

Test summary
Passed: 1
Failed: 0
[ooooooooook] 100.0% passed
Question 2
We believe Gary’s model is incorrect. In particular, we believe there to be a smaller chance
of heads. Which of the following statistics can we use during our simulation to test between the
model and our alternative? Assign
statistic_choice
as the correct answer.
1. The distance (absolute value) between the actual number of heads in 10 flips and the ex-
pected number of heads in 10 flips (5)
2. The expected number of heads in 10 flips
3. The actual number of heads we get in 10 flips

Out[126]:
1
Question 3
Define the function
coin_simulation_and_statistic
, which, given a sample size
and an array of model proportions (like the one you created in Q1), returns the number of heads
in one simulation of flipping the coin under the model specified in
model_proportions
.
Hint:
Think about how you can use the function
sample_proportions
.

Question 4
Use your function from above to simulate the flipping of 10 coins 5000 times under the pro-
portions that you specified in problem 1. Keep track of all of your statistics in
coin_statistics
.
16

In [131]:
coin_statistics
=
make_array()
repetitions
= 5000
for
i
in
np
.
arange(repetitions):
coin_statistics
=
np
.
append(coin_statistics, coin_simulation_and_statistic(
10
, co
coin_statistics
Out[131]:
array([3., 3., 7., ..., 4., 7., 4.])
In [132]:
_
=
ok
.
grade(
'
q5_4
'
)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Running tests
---------------------------------------------------------------------
Test summary
Passed: 1
Failed: 0
[ooooooooook] 100.0% passed
Let’s take a look at the distribution of statistics, using a histogram.
In [133]:
#Draw a distribution of statistics
Table()
.
with_column(
'
Coin Statistics
'
, coin_statistics)
.
hist()
/srv/app/venv/lib/python3.6/site-packages/matplotlib/axes/_axes.py:6462: UserWarning: The
'
norm
warnings.warn("The
'
normed
'
kwarg is deprecated, and has been "
17