PSTAT 5A Lab 1 - SOLUTIONS

Introduction to Python and JupyterHub

Author

Solution Key

Published

July 7, 2025

Lab 1 Solutions

This document provides complete solutions to all tasks in PSTAT 5A Lab 1.

Task 1 Solution

Objective: Rename your notebook from Untitled to Lab1

Steps:

  • Located the notebook in the file browser (appears as Untitled.ipynb)

  • Right-clicked on the notebook name

  • Selected “Rename” from the context menu

  • Changed the name to Lab1

  • Pressed Enter to confirm

  • Verified the title bar now shows Lab1.ipynb

Expected Result:

Your notebook should now be named Lab1.ipynb and this should be visible in both the file browser and the title bar.

Task 2 Solution

Objective: Create a Markdown cell with heading and a Code cell with basic arithmetic

Markdown Cell:

# Task 2

Code Cell:

2 + 2
4

Expected Result:

  • The code cell executes the arithmetic operation

  • Python displays the result 4 below the cell

  • A new empty code cell automatically appears below

  • The cell is marked as executed with a number like [1]

Task 3 Solution

Objective: Demonstrate syntax error and understand error messages

Markdown Cell:

# Task 3

Code Cell with Intentional Error:

2 plus 2

Expected Error Output:

  Cell In[2], line 1
    2 plus 2
      ^^^^
SyntaxError: invalid syntax

Explanation:

  • Python doesn’t understand plus as an operator

  • The ^^^^ points to where Python detected the problem

  • The error message tells us it’s a SyntaxError meaning invalid Python syntax

  • In Python, we must use + for addition, not the word plus

Corrected Version:

2 + 2  # This works correctly
4

Task 4 Solution

Objective: Compute mathematical expressions using Python**

Problem 1: \(\frac{2 + 3}{4 + 5^6}\)

Python Code:

(2 + 3) / (4 + 5**6)
0.0003199181009661527

Step by Step:

numerator = 2 + 3
print(f"Numerator: {numerator}")

denominator = 4 + 5**6
print(f"Denominator: {denominator}")

result = numerator / denominator
print(f"Final result: {result}")
Numerator: 5
Denominator: 15629
Final result: 0.0003199181009661527

Problem 2: \((1 - 3 \cdot 4^5)^6\)

Python Code:

(1 - 3 * 4**5)**6
838839550121163601921

Step by Step:

inner_exponent = 4**5
print(f"4^5 = {inner_exponent}")

multiplication = 3 * inner_exponent
print(f"3 * 4^5 = {multiplication}")

subtraction = 1 - multiplication
print(f"1 - 3 * 4^5 = {subtraction}")

final_result = subtraction**6
print(f"(1 - 3 * 4^5)^6 = {final_result}")
4^5 = 1024
3 * 4^5 = 3072
1 - 3 * 4^5 = -3071
(1 - 3 * 4^5)^6 = 838839550121163601921

Task 5 Solution

Objective: Understand module importing and fix NameError

Step 1: Code that produces error

sin(1)

Expected Error:

NameError: name 'sin' is not defined

Explanation: Python doesn’t recognize sin because the math functions aren’t loaded by default.

Step 2: Import module and retry

from math import *
sin(1)
0.8414709848078965

Alternative Solutions:

# Method 1: Import specific function
from math import sin
print(sin(1))

# Method 2: Import entire module
import math
print(math.sin(1))

# Method 3: Import with alias
import math as m
print(m.sin(1))
0.8414709848078965
0.8414709848078965
0.8414709848078965

All produce the same result: 0.8414709848078965

Task 6 Solution

Objective: Understand Python case sensitivity

Step 1: Variable assignment

my_variable = 5

Step 2: Wrong capitalization

print(My_variable)

Expected Error:

NameError: name 'My_variable' is not defined

Explanation: Python is case-sensitive, so My_variable ≠ my_variable

Step 3: Correct capitalization

print(my_variable)
5

Additional Examples:

# These are all different variables in Python
my_variable = 5
My_variable = 10
MY_VARIABLE = 15
my_Variable = 20

print(f"my_variable = {my_variable}")
print(f"My_variable = {My_variable}")
print(f"MY_VARIABLE = {MY_VARIABLE}")
print(f"my_Variable = {my_Variable}")
my_variable = 5
My_variable = 10
MY_VARIABLE = 15
my_Variable = 20

Task 7 Solution

Objective: Add descriptive comments to previous code

Examples of well-commented code from previous tasks:

# Task 2: Basic arithmetic
2 + 2  # Adding two integers

# Task 4: Complex mathematical expression
# Calculate (2 + 3) / (4 + 5^6)
numerator = 2 + 3  # Sum of 2 and 3
denominator = 4 + 5**6  # 4 plus 5 to the 6th power
result = numerator / denominator  # Final division
print(f"Result: {result}")

# Task 5: Import math module and use sin function
from math import *  # Import all math functions
angle_in_radians = 1  # Input angle in radians
sine_value = sin(angle_in_radians)  # Calculate sine
print(f"sin(1) = {sine_value}")

# Task 6: Variable assignment with proper naming
my_variable = 5  # Store the value 5 in my_variable
print(my_variable)  # Display the value

"""
This is a multi-line comment.
It can span multiple lines and is useful
for longer explanations or documentation.
"""

Good commenting practices demonstrated:

  • Explain what the code does

  • Clarify complex calculations

  • Document variable purposes

  • Use both inline (#) and block (""") comments

Task 8 Solution

Objective: Explore Python data types using the type() function

Code and Expected Outputs:

print(type(1))           # Output: <class 'int'>
print(type(1.1))         # Output: <class 'float'>
print(type("hello"))     # Output: <class 'str'>
<class 'int'>
<class 'float'>
<class 'str'>

Additional Examples:

# More data type examples
print("Integer:", type(42))
print("Float:", type(3.14159))
print("String with single quotes:", type('Python'))
print("String with double quotes:", type("Programming"))
print("Boolean True:", type(True))
print("Boolean False:", type(False))
print("List:", type([1, 2, 3]))
print("Tuple:", type((1, 2, 3)))
print("Dictionary:", type({"key": "value"}))
Integer: <class 'int'>
Float: <class 'float'>
String with single quotes: <class 'str'>
String with double quotes: <class 'str'>
Boolean True: <class 'bool'>
Boolean False: <class 'bool'>
List: <class 'list'>
Tuple: <class 'tuple'>
Dictionary: <class 'dict'>

Task 9 Solution

Objective: Practice variable assignment, updating, and calculations

Markdown cell:

# Task 9

Step 2: Initial variable assignments

course = "PSTAT 5A"
num_sections = 4
section_capacity = 25

Step 3: Update num_sections (correct approach)

num_sections = num_sections + 1
print(f"Updated number of sections: {num_sections}")
# Alternative: num_sections += 1
# Alternative: num_sections = 4 + 1
Updated number of sections: 5

Step 4: Predict and test expressions

print(type(course))           # Expected: <class 'str'>
print(type(num_sections))     # Expected: <class 'int'>
print(num_sections * section_capacity) # Expected: 125
<class 'str'>
<class 'int'>
125

Step 5: Calculate course capacity

course_capacity = num_sections * section_capacity
print(f"Course: {course}")
print(f"Number of sections: {num_sections}")
print(f"Capacity per section: {section_capacity}")
print(f"Total course capacity: {course_capacity}")
Course: PSTAT 5A
Number of sections: 5
Capacity per section: 25
Total course capacity: 125

Complete Solution with Comments:

# Step 2: Initial variable assignments
course = "PSTAT 5A"          # Course name as string
num_sections = 4             # Initial number of sections
section_capacity = 25        # Maximum students per section

# Step 3: A new section has been added
num_sections = num_sections + 1  # Increment by 1, now equals 5

# Step 4: Testing expressions with predictions
print("Testing type() function:")
print(f"type(course) = {type(course)}")  # Expected: <class 'str'>
print(f"type(num_sections) = {type(num_sections)}")  # Expected: <class 'int'>
print(f"num_sections * section_capacity = {num_sections * section_capacity}")  # Expected: 125

# Step 5: Calculate total course capacity
course_capacity = num_sections * section_capacity  # 5 × 25 = 125
print(f"\nFinal Results:")
print(f"Course: {course}")
print(f"Total sections: {num_sections}")
print(f"Capacity per section: {section_capacity}")
print(f"Total course capacity: {course_capacity} students")
Testing type() function:
type(course) = <class 'str'>
type(num_sections) = <class 'int'>
num_sections * section_capacity = 125

Final Results:
Course: PSTAT 5A
Total sections: 5
Capacity per section: 25
Total course capacity: 125 students

Summary of Key Concepts Learned

✅ JupyterHub Environment

  • Creating and renaming notebooks

  • Understanding cell types (Code vs Markdown)

  • Running cells with ▶️ button or Shift+Enter

  • Navigating the interface

✅ Python Basics

  • Arithmetic operations: +, -, *, /, **

  • Order of operations: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction

  • Error reading: Understanding SyntaxError and NameError messages

✅ Variables and Data Types

  • Variable assignment: variable_name = value

  • Case sensitivity: my_var ≠ My_var

  • Basic types: int, float, str, bool

  • Type checking: type() function

✅ Modules and Imports

  • Import syntax: from module import * or import module

  • Using functions: After importing, functions become available

  • Math module: Contains mathematical functions like sin(), cos(), etc.

✅ Comments and Documentation

  • Inline comments: # This is a comment

  • Block comments: """Multi-line comment"""

  • Purpose: Document code for yourself and others

✅ Programming Best Practices

  • Write descriptive variable names

  • Add comments to explain complex logic

  • Test your code incrementally

  • Read and understand error messages

  • Use existing variables in calculations when possible

Next Steps

In Lab 2, you’ll learn about:

  • Python functions and how to create them

  • Data structures (lists, dictionaries)

  • Control flow (if statements, loops)

  • More advanced programming concepts

Great work completing Lab 1! You now have the foundation needed for statistical programming in Python.