Probability Programming HW 2025

Info

• Instructor : Professor Rung-Hung Gau
• Student Name : Jing-Xuan Chen
• Student ID : 113511170
• Department : NYCU EE

Abstract

The square is randomly thrown on the x-y plane with its center fixed on the y axis.

And Y and θ are independent.

Objectives

The goal is to get the E[qn] and E[W] via conducting the simulation for the large enough number of times.

• In Task 1, Y and θ are uniformly distributed. Figure 1 is created to show qn, the sum of Bernoulli random variable ak, for k=1, 2…n.

• Task 2 holds a difference from Task 1. θ is still uniformly distributed, yet Y is not.

• Task 3 requires finding the expected value of W, which is the area of square that below x axis.

• Merge all the program in main code NYCU-113511170.py.

Python Code

• NYCU-113511170.py : main program

• figure01.py : Task 1

• figure02.py : Task 2

• figure03.py : Task 3

• verify_area.py :

  To verify if E[W] obtained from figure3.py is correct.

  The file is not for simulation but for direct computing the double integration.

Guide

1. Enter the main code NYCU-113511170.py

2. If enter 1, figure 1 is shown.

And the Simulated Result is printed:

3. If enter 2, figure 2 is shown.

4. If enter 3, figure 3 is shown.

5. If enter 4, all the figure will be saved and named 113511170_figure0X.png.

6. If enter 5, exit the program.

Homework Descriptions