Generating random samples in NumPy - Mini Project: Build & Apply

Generating Random Samples with NumPy

📖 Scenario: Imagine you are a data scientist working on a project where you need to simulate data for testing. You want to create random samples from a normal distribution to mimic real-world measurements.

🎯 Goal: Learn how to generate random samples using NumPy's random module and display the generated data.

📋 What You'll Learn

Create a NumPy array of random samples from a normal distribution

Set the mean and standard deviation for the distribution

Generate a specific number of samples

Print the generated samples

💡 Why This Matters

🌍 Real World

Generating random samples is useful for simulating data when real data is not available or for testing algorithms.

💼 Career

Data scientists often need to create synthetic data to test models or understand statistical properties.

1

Import NumPy and set up sample size

Import the numpy library as np and create a variable called sample_size with the value 10.

NumPy

# Import numpy as np
# Create a variable sample_size and set it to 10
# Your code here

Hint

Use import numpy as np to import NumPy. Then create sample_size = 10.

2

Set mean and standard deviation

Create two variables: mean with value 0 and std_dev with value 1 to represent the mean and standard deviation of the normal distribution.

NumPy

import numpy as np
sample_size = 10
# Create mean variable with value 0
# Create std_dev variable with value 1
# Your code here

Hint

Set mean = 0 and std_dev = 1.

3

Generate random samples

Use np.random.normal with parameters mean, std_dev, and sample_size to create a variable called samples that holds the random samples.

NumPy

import numpy as np
sample_size = 10
mean = 0
std_dev = 1
# Generate samples using np.random.normal and assign to samples
# Your code here

Hint

Call np.random.normal(mean, std_dev, sample_size) and assign it to samples.

4

Print the generated samples

Print the variable samples to display the generated random numbers.

NumPy

import numpy as np
sample_size = 10
mean = 0
std_dev = 1
samples = np.random.normal(mean, std_dev, sample_size)
# Print the samples
# Your code here

Hint

Use print(samples) to show the array of random numbers.

Practice

1. What does the numpy.random.choice function do?

easy

A. It calculates the mean of an array.

B. It selects random elements from a given array or list.

C. It sorts an array in ascending order.

D. It reshapes an array into a new shape.

Solution

1. Step 1: Understand the function purpose

   numpy.random.choice is designed to pick random elements from a given array or list.

2. Step 2: Compare with other options

   Sorting, calculating mean, and reshaping are different numpy functions, not related to random sampling.

3. Final Answer:

   It selects random elements from a given array or list. -> Option B

4. Quick Check:

   Random sampling = selecting elements randomly [OK]

Hint: Remember: choice means picking randomly from data [OK]

Common Mistakes:

• Confusing choice with sorting or reshaping functions
• Thinking it calculates statistics like mean
• Assuming it modifies array shape

2. Which of the following is the correct syntax to randomly select 3 elements from array arr without replacement using numpy?

easy

A. numpy.random.choice(arr, 3, replace=True)

B. numpy.choice(arr, size=3, replace=False)

C. numpy.random.choice(arr, size=3, replace=False)

D. numpy.random.choice(arr, size=3, replace=True)

Solution

1. Step 1: Identify correct function and parameters

   The function is numpy.random.choice. To select 3 elements without replacement, use size=3 and replace=False.

2. Step 2: Check each option

   numpy.random.choice(arr, size=3, replace=False) uses correct function and parameters. numpy.random.choice(arr, 3, replace=True) uses replacement True (wrong). numpy.choice(arr, size=3, replace=False) uses wrong function name. numpy.random.choice(arr, size=3, replace=True) uses replacement True (wrong).

3. Final Answer:

   numpy.random.choice(arr, size=3, replace=False) -> Option C

4. Quick Check:

   Correct syntax = choice + size + replace=False [OK]

Hint: Use replace=False to avoid repeated picks [OK]

Common Mistakes:

• Using replace=True when no repeats wanted
• Misspelling function name as numpy.choice
• Passing size as positional without keyword

3. What is the output of this code?

import numpy as np
np.random.seed(0)
arr = np.array([10, 20, 30, 40])
sample = np.random.choice(arr, size=2, replace=False)
sample_sorted = np.sort(sample)
sample_sorted.tolist()

medium

A. [10, 40]

B. [10, 20]

C. [20, 40]

D. [30, 40]

Solution

1. Step 1: Understand random seed and choice

   Setting seed to 0 fixes randomness. Using choice with size=2 and replace=False picks 2 unique elements from [10,20,30,40].

2. Step 2: Determine chosen elements and sort

   With seed 0, the chosen elements are [10, 40]. Sorting gives [10, 40].

3. Final Answer:

   [10, 40] -> Option A

4. Quick Check:

   Seed 0 + choice + sort = [10, 40] [OK]

Hint: Seed fixes output; sort to order chosen elements [OK]

Common Mistakes:

• Ignoring seed and expecting different output
• Not sorting before converting to list
• Assuming replacement allows duplicates

4. The following code throws an error. What is the cause?

import numpy as np
arr = np.array([1, 2, 3])
sample = np.random.choice(arr, size=5, replace=False)

medium

A. Incorrect function name used.

B. Array contains integers instead of floats.

C. Missing import statement for numpy.

D. Size is larger than array length without replacement.

Solution

1. Step 1: Analyze parameters and array size

   The array has 3 elements, but size=5 is requested without replacement.

2. Step 2: Understand replacement=False effect

   Without replacement, you cannot pick more elements than exist. This causes a ValueError.

3. Final Answer:

   Size is larger than array length without replacement. -> Option D

4. Quick Check:

   Sampling more than available without replace=False causes error [OK]

Hint: Check if sample size > array length when replace=False [OK]

Common Mistakes:

• Assuming replacement=True by default
• Ignoring array length vs sample size
• Thinking data type causes error

5. You want to simulate rolling a weighted 6-sided die 10 times using numpy, where side 6 is twice as likely as others. Which code correctly generates this sample?

hard

A. np.random.choice([1,2,3,4,5,6], size=10, replace=True, p=[1/7,1/7,1/7,1/7,1/7,2/7])

B. np.random.choice([1,2,3,4,5,6], size=10, replace=False, p=[1/6]*6)

C. np.random.choice([1,2,3,4,5,6], size=10, replace=True)

D. np.random.choice([1,2,3,4,5,6], size=10, replace=True, p=[1/6,1/6,1/6,1/6,1/6,1/6])

Solution

1. Step 1: Understand weighted probabilities

   Side 6 should be twice as likely, so probabilities sum to 1 with side 6 having weight 2/7 and others 1/7 each.

2. Step 2: Check sampling parameters

   Sampling 10 times with replacement is needed to allow repeats. np.random.choice([1,2,3,4,5,6], size=10, replace=True, p=[1/7,1/7,1/7,1/7,1/7,2/7]) uses correct probabilities and replace=True.

3. Step 3: Verify other options

   The code with replace=False, p=[1/6]*6 incorrectly prevents repeats needed for multiple rolls. The codes with uniform probabilities (explicit [1/6,1/6,1/6,1/6,1/6,1/6] or none specified) do not weight side 6 twice as likely.

4. Final Answer:

   np.random.choice([1,2,3,4,5,6], size=10, replace=True, p=[1/7,1/7,1/7,1/7,1/7,2/7]) -> Option A

5. Quick Check:

   Weighted probabilities + replace=True for repeated rolls [OK]

Hint: Use p= with weights summing to 1 and replace=True [OK]

Common Mistakes:

• Using replace=False for multiple rolls
• Not setting probabilities for weighted sides
• Using equal probabilities when weights differ