Uniform distribution in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of uniform random sample generation

What is the output of this code snippet that generates 3 random numbers from a uniform distribution between 0 and 1?

SciPy

from scipy.stats import uniform
sample = uniform.rvs(size=3, random_state=42)
print([round(x, 2) for x in sample])

A [0.37, 0.95, 0.73, 0.60]

B [0.37, 0.95, 0.73]

C [0.42, 0.58, 0.91]

D [0.73, 0.37, 0.95]

💡 Hint

Use the random_state to get reproducible results and round the output to 2 decimals.

The uniform.rvs function with random_state=42 produces the same 3 values every time. Rounded to 2 decimals, they are [0.37, 0.95, 0.73].

❓ data_output

intermediate

Mean and variance of uniform distribution

What are the mean and variance of a uniform distribution between 2 and 5?

SciPy

from scipy.stats import uniform
rv = uniform(loc=2, scale=3)
mean = rv.mean()
var = rv.var()
print(round(mean, 2), round(var, 2))

A 3.0 1.0

B 3.5 1.0

C 2.5 0.75

D 3.5 0.75

💡 Hint

Mean is midpoint; variance is (scale^2)/12.

Mean = (2 + 5)/2 = 3.5; Variance = (3^2)/12 = 9/12 = 0.75.

❓ visualization

advanced

Plotting PDF of uniform distribution

Which option produces the correct plot of the probability density function (PDF) of a uniform distribution from 0 to 4?

SciPy

import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import uniform
x = np.linspace(-1, 5, 500)
rv = uniform(loc=0, scale=4)
plt.plot(x, rv.pdf(x))
plt.title('Uniform PDF from 0 to 4')
plt.show()

A A flat line at height 0.25 between 0 and 4, zero elsewhere

B A bell-shaped curve centered at 2

C A line increasing from 0 to 4

D A line decreasing from 0 to 4

💡 Hint

Uniform PDF is constant between loc and loc+scale.

The PDF of uniform(0,4) is 1/4=0.25 between 0 and 4, zero outside. So the plot is a flat line at 0.25 in that range.

🧠 Conceptual

advanced

Effect of scale parameter on uniform distribution

If you increase the scale parameter of a uniform distribution while keeping the location fixed, what happens to the variance?

A Variance stays the same

B Variance decreases linearly with scale

C Variance increases quadratically with scale

D Variance increases linearly with scale

💡 Hint

Variance formula involves square of scale.

Variance of uniform(loc, scale) is (scale^2)/12, so it grows with the square of scale.

🔧 Debug

expert

Identify the error in uniform distribution sampling code

What error does this code raise? from scipy.stats import uniform sample = uniform.rvs(loc=1, scale=-2, size=5) print(sample)

SciPy

from scipy.stats import uniform
sample = uniform.rvs(loc=1, scale=-2, size=5)
print(sample)

A ValueError: scale parameter must be positive

B TypeError: size must be an integer

C No error, prints 5 samples

D RuntimeWarning: invalid value encountered

💡 Hint

Scale parameter cannot be negative for uniform distribution.

The scale parameter must be positive; negative scale raises ValueError.