Random variable generation in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of generating normal random variables

What is the output of this code snippet that generates 3 samples from a normal distribution with mean 0 and standard deviation 1 using scipy.stats?

SciPy

from scipy.stats import norm
samples = norm.rvs(loc=0, scale=1, size=3)
samples_rounded = [round(x, 2) for x in samples]
samples_rounded

A [0.0, 0.0, 0.0]

B A list of 3 float numbers close to 0 but random, e.g., [0.12, -0.45, 1.03]

C [0.5, -1.2, 0.3]

D [1, 1, 1]

💡 Hint

The output is random but will be three float numbers around zero.

The norm.rvs function generates random samples from a normal distribution. Since the mean is 0 and std dev is 1, the values will be floats near zero but random each time.

❓ data_output

intermediate

Shape of generated random variable array

What is the shape of the array generated by this code that samples from a uniform distribution?

SciPy

from scipy.stats import uniform
samples = uniform.rvs(loc=0, scale=10, size=(4, 2))
samples.shape

A (4, 2)

B (2, 4)

C (8,)

D (4,)

💡 Hint

The size parameter defines the shape of the output array.

The size=(4, 2) argument tells scipy to generate a 2D array with 4 rows and 2 columns.

🔧 Debug

advanced

Identify the error in random variable generation code

What error does this code raise when trying to generate samples from a binomial distribution?

SciPy

from scipy.stats import binom
samples = binom.rvs(n=10, p=0.5, size='5')

A TypeError: 'str' object cannot be interpreted as an integer

B ValueError: Probability p must be between 0 and 1

C SyntaxError: invalid syntax

D No error, code runs fine

💡 Hint

Check the type of the size argument.

The size parameter must be an integer or tuple of integers, not a string. Passing '5' causes a TypeError.

🚀 Application

advanced

Generating and summarizing Poisson random variables

You generate 1000 samples from a Poisson distribution with lambda=3. Which option correctly describes the expected mean and variance of the samples?

SciPy

from scipy.stats import poisson
samples = poisson.rvs(mu=3, size=1000)
mean_val = samples.mean()
var_val = samples.var()

A Mean close to 0, variance close to 3

B Mean close to 3, variance close to 0

C Mean and variance both close to 3

D Mean and variance both close to 0

💡 Hint

For Poisson distribution, mean equals variance.

Poisson distribution has mean and variance equal to lambda (mu). So both mean and variance should be near 3.

🧠 Conceptual

expert

Effect of random seed on reproducibility

Which statement about setting a random seed before generating random variables with scipy.stats is correct?

A Setting the seed has no effect on random variable generation.

B Setting the seed makes the random numbers more random.

C Setting the seed disables randomness and returns constant values.

D Setting the seed ensures the same random numbers are generated every time the code runs.

💡 Hint

Think about reproducibility in experiments.

Setting a random seed initializes the random number generator to a fixed state, so the same sequence of random numbers is produced each run.