1. Programming with data Lab 3
Wednesday, 14 Nov. 2018
Stelios Sotiriadis
Prof. Alessandro Provetti

2. Visualization and Probabilities

3. Matplotlib For 2D data, visualization is readily available.
Against the range domain:
from matplotlib import pyplot as plt
plt.plot(values, color='green', marker='o', linestyle='solid')
plt.title("Visualization of my list")
plt.xlabel('position')
plt.ylabel('value')
plt.show()

4. Matplotlib
import matplotlib.pyplot as plt plt.plot([1,2,3,4,5,6], [1,4,9,16,25,36], 'ro') plt.axis([0, 6, 0, 20]) plt.show()

5. Lab exercises

6. Present your results on binSearch
Generate lists of random integers, in ascending order, for n=1k, 2k, 4k, 8k.
Generate random keys.
Time the cumulative time of search only, find the average for each size.
Plot it using matplotlib
Save on a file

7. How platform and I/O influence timing
Run the same experiment by:
omitting any print command
Are results drastically different?
Run the same experiment on a different computer.
Plot the new results over a shorter range, a percentage of the previous results.

8. Exercise 1: Probabilities
Consult Joel Grus’ Data Science from Scratch for the ‘probability of having two baby girls example’
Run the program!

9. Exercise 2: Simulate coin tosses
Develop a function simulateTosses(n) that simulates n coin tosses as many as the user wants.
Coin toss can be Head or Tail (randomly decided) e.g. simulateTosses(100)
The output is the probability of having heads or tails in n tosses, in our example the probability of heads in 100 tosses could be for example 0.49 etc.
Develop a function to run 100 times the simulateTosses(100). In other words, 100 repetitions where each one is the probability of heads when we toss 100 times.
The function could be called: moreSimulations(n1,n2), where n1 refers to the number of times we want to simulate the simulateTosses(n).
Generate a diagram like this (x axis: 0-n(100), y axis: 0-1).
What do you observe?
Increase the numbers!
coinTosser.py

10. Exercise 3: Study secretary problem
The probability of selecting the best applicant in the classical secretary problem converges toward 1/e ≈ (approx.)
Study the secretary.py code.
The code solves the secretary problem in Python!
Run the secretary problem by comparing two optimal stopping strategies n/e and 𝑛 .
secretary.py | secretary1.py