Programming Assignment 3: Drawing Balls From an Urn
Programming Assignment 3: Drawing Balls From an Urn
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tl;dr: There are 3 tasks and 1 conclusion task waiting for you (scroll down for more information). CourseNana.COM
Introduction
You have an urn. Initially there are R red balls and B blue balls in the urn. You would like to randomly draw a ball from an urn, for exactly N times. CourseNana.COM
# Just in case you need to import some packages.
import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt
plt.style.use("seaborn-v0_8")
Task 1: With Replacement (1 point)
Suppose each time after you draw a ball from an urn, you put the ball back to the urn. Please write a function drawing_balls_with_replacement(R, B, N, rep) that simulates the above experiment for rep times. For each experiment, you record the number of red balls being drawn. Then, your function plots a histogram on the number of red balls being drawn for the scenario.
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Return Value
Your function returns the average number of red balls being drawn in an experiment. CourseNana.COM
def drawing_balls_with_replacement(R = 100, B = 100, N = 100, rep = 10000):
# a sample implementation, feel free to re-write the whole thing.
def one_experiment(R, B, N):
"""Your code here."""
return np.random.randint(1, N) # change me!
exps = [one_experiment(R, B, N) for _ in range(rep)]
plt.hist(exps, bins=range(min(exps)-10, max(exps)+10), edgecolor='k', alpha=0.5)
return np.mean(exps)
Testing
We will test your function with the following parameters. CourseNana.COM
# Test 1.1
drawing_balls_with_replacement(100, 100, 100, 10000)
# Test 1.2
drawing_balls_with_replacement(100, 300, 100, 10000)
Task 2: Without Replacement (1 point)
Suppose each time after you draw a ball from an urn, you DO NOT put the ball back to the urn. Please write a function drawing_balls_without_replacement(R, B, N, rep) that simulates the above experiment for rep times. For each experiment, you record the number of red balls being drawn. Then, your function plots a histogram on the number of red balls being drawn for the scenario.
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Return Value
Your function returns the average number of red balls being drawn in an experiment. CourseNana.COM
def drawing_balls_without_replacement(R = 100, B = 100, N = 100, rep = 10000):
"""Your code here."""
return 0.0
Testing
Now, we compare the experiments on whether or not we put the ball back into the urn. CourseNana.COM
# Test 2.1
avg1 = drawing_balls_with_replacement(100, 100, 100, 10000)
avg2 = drawing_balls_without_replacement(100, 100, 100, 10000)
print(avg1, avg2)
# Test 2.2
avg1 = drawing_balls_with_replacement(100, 300, 200, 10000)
avg2 = drawing_balls_without_replacement(100, 300, 200, 10000)
print(avg1, avg2)
# Test 2.3
avg1 = drawing_balls_with_replacement(100, 300, 300, 10000)
avg2 = drawing_balls_without_replacement(100, 300, 300, 10000)
print(avg1, avg2)
Task 3: With Duplication (1 point)
Suppose each time after you draw a ball from an urn, you put an additional ball of the same color back to the urn. Please write a function drawing_balls_with_duplication(R, B, N, rep) that simulates the above experiment for rep times. For each experiment, you record the number of red balls being drawn. Then, your function plots a histogram on the number of red balls being drawn for the scenario.
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Return Value
Your function returns the average number of red balls being drawn in an experiment. CourseNana.COM
def drawing_balls_with_duplication(R = 100, B = 100, N = 100, rep = 10000):
"""Your code here."""
return 0.0
Testing
Please design 3 meaningful tests, the choice of the parameters is up to you. CourseNana.COM
# Test 3.1
avg1 = drawing_balls_with_replacement(100, 100, 100, 10000)
avg2 = drawing_balls_without_replacement(100, 100, 100, 10000)
avg3 = drawing_balls_with_duplication(100, 100, 100, 10000)
print(avg1, avg2, avg3)
# Test 3.2
# Test 3.3
Task 4: Conclusion (1 point)
What do you observe from the above figures? Are there possible explanations about you observation? (Any reasonable observation deserves full credits.) CourseNana.COM
