Program to Solve Probability Questions Assignment Solution.

Instructions

Objective

Write a Python assignment program to solve probability questions in Python. You are tasked with creating a program that calculates probabilities based on given inputs. Utilize Python's mathematical libraries to handle complex probability calculations efficiently. Your assignment should showcase your understanding of fundamental probability concepts and your ability to translate them into functional code. Ensure your program is well-documented, with clear explanations of the implemented logic and any assumptions made. This assignment will not only assess your Python programming skills but also your grasp of probability theory. Keep the code concise, organized, and thoroughly tested to demonstrate your proficiency.

Requirements and Specifications

program to solve probability questions in python 1

program to solve probability questions in python 2

Source Code

import random
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import math
def Tpath(T, sigma, p, x0):
 """
 QUESTION 1: Simulate the path of T
 """
 # Create the list with the initial value
 x = np.zeros(T+1)
 # Now, simulate
 for t in range(1,T+1):
 # Generate epsilon
 prob = random.uniform(0,1)
 epsilon = 1 if prob <= p else -1
 # Generate value
 xt = x[t-1] + sigma*epsilon
 # Append
 x[t] = xt
 # Return
 return x
def stock_betas(filename):
 # First, open file
 data = pd.read_excel(filename, engine='openpyxl', skiprows = 1)
 sp500 = data.iloc[:,1].to_numpy()
 P = data.iloc[:,2:].to_numpy()
 # Now for each stock calculate all RTs and beta
 betas = []
 for i in range(P.shape[1]):
 prices = P[:,i]
 x = []
 y = []
 xy = []
 xx = []
 # Calculate RTs
 for t in range(1,len(prices)):
 Pt = prices[t]
 Ptold = prices[t-1]
 if not math.isnan(Pt) and not math.isnan(Ptold) and Pt >= 0 and Ptold > 0:
 Rt = (Pt-Ptold)/Ptold
 y.append(Rt)
 dsp500 = (sp500[t]-sp500[t-1])/sp500[t-1]
 x.append(dsp500)
 xy.append(Rt*dsp500)
 xx.append(dsp500**2)
 # Now calculate
 beta = (len(x) * sum(xy) - sum(x) * sum(y)) / (len(x)*sum(xx) - sum(x) ** 2)
 betas.append(beta)
 return betas
if __name__ == '__main__':
 # Question 2
 T = 120
 sigma = 0.6
 p = 0.5
 x0 = 10
 # Run the simulation of 1,000,000 cases
 prob = 0.0
 N = 10000
 for _ in range(N):
 x = Tpath(T, sigma, p, x0)
 # Pick the number of times that x is less than x0
 prob += len(np.where(x <= 0.75*x0)[0])/(T+1)
 prob = prob/N
 print("The probability that xt drops at least 25% below its initial value at least once is {:.4f}%".format(prob*100.0))
 """ Question 3 """
 # generate a new path
 x = Tpath(T, sigma, p, x0)
 plt.figure()
 plt.plot(range(T+1), x)
 plt.xlabel('Time (month)')
 plt.ylabel('Probability')
 plt.title('Probability vs. Time')
 plt.grid(True)
 plt.show()
 """ Question 4 """
 betas = stock_betas('stockprices2020b.xlsx')
 print(betas)

Python Program to Solve Probability Questions Assignment Solution.

Instructions

Requirements and Specifications