Probability density and cumulative functions in SciPy - Mini Project: Build & Apply

Probability Density and Cumulative Functions with SciPy

📖 Scenario: You work as a data analyst for a company that studies daily rainfall amounts. You want to understand the likelihood of different rainfall amounts using a common probability model called the normal distribution.

🎯 Goal: Build a small program that uses SciPy to calculate the probability density and cumulative probability for specific rainfall amounts using the normal distribution.

📋 What You'll Learn

Create a normal distribution with mean 50 and standard deviation 10

Calculate the probability density function (PDF) for rainfall amounts 40, 50, and 60

Calculate the cumulative distribution function (CDF) for rainfall amounts 40, 50, and 60

Print the PDF and CDF results clearly

💡 Why This Matters

🌍 Real World

Understanding rainfall probabilities helps in planning for agriculture, water management, and flood prevention.

💼 Career

Data analysts and scientists often use probability distributions to model and predict real-world events.

1

Create the rainfall amounts list

Create a list called rainfall_amounts with the exact values 40, 50, and 60.

SciPy

# Create the list rainfall_amounts with values 40, 50, and 60
# Your code here

Need a hint?

Use square brackets to create a list with the numbers 40, 50, and 60 inside.

2

Set up the normal distribution parameters

Create two variables: mean set to 50 and std_dev set to 10.

SciPy

rainfall_amounts = [40, 50, 60]
# Create mean = 50 and std_dev = 10
# Your code here

Need a hint?

Use simple assignment to create mean and std_dev variables with the given numbers.

3

Calculate PDF and CDF values using SciPy

Import norm from scipy.stats. Then create a normal distribution object called normal_dist using mean and std_dev. Use normal_dist.pdf() to calculate the PDF values for rainfall_amounts and store in pdf_values. Use normal_dist.cdf() to calculate the CDF values for rainfall_amounts and store in cdf_values.

SciPy

rainfall_amounts = [40, 50, 60]
mean = 50
std_dev = 10
# Import norm from scipy.stats
# Create normal_dist with mean and std_dev
# Calculate pdf_values for rainfall_amounts
# Calculate cdf_values for rainfall_amounts
# Your code here

Need a hint?

Use norm(loc=mean, scale=std_dev) to create the distribution. Then call pdf() and cdf() with the list rainfall_amounts.

4

Print the PDF and CDF results

Print the pdf_values and cdf_values variables. Use print() statements with clear labels: "PDF values:" and "CDF values:".

SciPy

from scipy.stats import norm

rainfall_amounts = [40, 50, 60]
mean = 50
std_dev = 10

normal_dist = norm(loc=mean, scale=std_dev)
pdf_values = normal_dist.pdf(rainfall_amounts)
cdf_values = normal_dist.cdf(rainfall_amounts)
# Print PDF values with label
# Print CDF values with label
# Your code here

Need a hint?

Use two print statements. Print the label first, then the variable.