Random sampling distributions in NumPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of sampling from a normal distribution

What is the shape of the array produced by this code?

NumPy

import numpy as np
sample = np.random.normal(loc=0, scale=1, size=(5, 3))
print(sample.shape)

A (5, 3)

B (3, 5)

C (5,)

D (15,)

💡 Hint

The size parameter defines the shape of the output array.

The size=(5,3) argument creates a 2D array with 5 rows and 3 columns.

❓ data_output

intermediate

Mean of samples from uniform distribution

What is the approximate mean of the samples generated by this code?

NumPy

import numpy as np
samples = np.random.uniform(low=10, high=20, size=10000)
print(round(samples.mean(), 1))

A 15.0

B 10.0

C 20.0

D 5.0

💡 Hint

The mean of a uniform distribution is the midpoint between low and high.

The mean of uniform(10, 20) is (10 + 20) / 2 = 15.

❓ visualization

advanced

Histogram shape of binomial samples

Which histogram shape best describes the samples from this binomial distribution?

NumPy

import numpy as np
import matplotlib.pyplot as plt
samples = np.random.binomial(n=10, p=0.5, size=1000)
plt.hist(samples, bins=range(12), edgecolor='black')
plt.show()

A Single spike at 10

B Symmetric bell-shaped around 5

C Skewed heavily to the right

D Uniform flat distribution

💡 Hint

Binomial with p=0.5 tends to be symmetric around n*p.

The binomial distribution with n=10 and p=0.5 is symmetric and peaks near 5.

🧠 Conceptual

advanced

Effect of sample size on sample mean variance

If you increase the sample size from 10 to 1000 when sampling from a normal distribution, what happens to the variance of the sample mean?

A It stays the same because variance depends only on the distribution

B It increases because more data adds more variability

C It decreases because larger samples give more stable means

D It becomes zero because large samples have no variance

💡 Hint

Think about how averaging many values affects variability.

The variance of the sample mean decreases as sample size increases, making the mean more stable.

🔧 Debug

expert

Identify the error in random sampling code

What error does this code raise when run?

NumPy

import numpy as np
samples = np.random.normal(loc=0, scale=1, size=-5)
print(samples)

A No error, prints an empty array

B TypeError: size must be an integer or tuple of integers

C SyntaxError: invalid syntax

D ValueError: negative dimensions are not allowed

💡 Hint

Check the size parameter for validity.

Negative size is invalid and raises a ValueError in numpy random functions.