Poisson distribution in SciPy - Mini Project: Build & Apply

Understanding Poisson Distribution with SciPy

📖 Scenario: Imagine you work at a call center. You want to understand how many calls you might get in an hour. The number of calls follows a pattern called the Poisson distribution, which helps predict how often events happen in a fixed time.

🎯 Goal: You will create a small program to calculate the probability of getting a certain number of calls in an hour using the Poisson distribution from the scipy library.

📋 What You'll Learn

Create a variable with the average number of calls per hour

Import the Poisson distribution function from scipy.stats

Calculate the probability of getting exactly 3 calls in an hour

Print the calculated probability

💡 Why This Matters

🌍 Real World

Poisson distribution is used to model events like calls, arrivals, or errors happening randomly over time.

💼 Career

Data scientists use Poisson distribution to analyze and predict event counts in fields like customer service, traffic flow, and quality control.

1

Set the average number of calls

Create a variable called average_calls and set it to 5, which is the average number of calls received per hour.

SciPy

# Create the variable average_calls and set it to 5
# Your code here

Hint

The average number of calls is a number, so just assign 5 to average_calls.

2

Import Poisson distribution from scipy.stats

Import the poisson function from the scipy.stats module.

SciPy

average_calls = 5
# Import poisson from scipy.stats
# Your code here

Hint

Use from scipy.stats import poisson to import the Poisson distribution function.

3

Calculate the probability of exactly 3 calls

Use the poisson.pmf function with average_calls and 3 to calculate the probability of getting exactly 3 calls. Store the result in a variable called prob_3_calls.

SciPy

average_calls = 5
from scipy.stats import poisson
# Calculate probability of exactly 3 calls and store in prob_3_calls
# Your code here

Hint

Use poisson.pmf(3, average_calls) to get the probability of 3 calls.

4

Print the probability result

Print the value of prob_3_calls to see the probability of exactly 3 calls in an hour.

SciPy

average_calls = 5
from scipy.stats import poisson
prob_3_calls = poisson.pmf(3, average_calls)
# Print the probability of exactly 3 calls
# Your code here

Hint

Use print(prob_3_calls) to display the probability.

Practice

1. What does the Poisson distribution model in data science?

easy

A. The probability of a variable being normally distributed

B. The average value of a continuous variable

C. The relationship between two categorical variables

D. The number of events happening in a fixed interval of time or space

Solution

1. Step 1: Understand the Poisson distribution concept

   The Poisson distribution is used to model counts of events that happen independently in a fixed interval of time or space.

2. Step 2: Match the concept to the options

   The number of events happening in a fixed interval of time or space correctly describes this as the number of events in a fixed interval, while others describe unrelated concepts.

3. Final Answer:

   The number of events happening in a fixed interval of time or space -> Option D

4. Quick Check:

   Poisson models event counts in intervals = A [OK]

Hint: Poisson counts events in fixed intervals, not averages or categories [OK]

Common Mistakes:

• Confusing Poisson with normal distribution
• Thinking Poisson models averages instead of counts
• Mixing Poisson with categorical data analysis

2. Which of the following is the correct way to import the Poisson distribution from scipy.stats?

easy

A. from scipy.stats import poisson

B. import poisson from scipy.stats

C. from scipy import poisson.stats

D. import scipy.poisson

Solution

1. Step 1: Recall correct Python import syntax

   Python imports use 'from module import object' format. The Poisson distribution is in scipy.stats as 'poisson'.

2. Step 2: Check each option's syntax

   from scipy.stats import poisson uses correct syntax. Options A, B, and C have incorrect import statements.

3. Final Answer:

   from scipy.stats import poisson -> Option A

4. Quick Check:

   Correct import syntax = D [OK]

Hint: Use 'from scipy.stats import poisson' to import Poisson [OK]

Common Mistakes:

• Using wrong import order or keywords
• Trying to import from wrong submodules
• Using 'import' instead of 'from ... import ...'

3. What is the output of this code?

from scipy.stats import poisson
rv = poisson(mu=3)
prob = rv.pmf(2)
print(round(prob, 3))

medium

A. 0.2240

B. 0.224

C. 0.149

D. 0.050

Solution

1. Step 1: Understand the pmf function with mu=3 and k=2

   The pmf gives the probability of exactly k=2 events when the average rate mu=3.

2. Step 2: Calculate the Poisson pmf for k=2, mu=3

   Using formula: P(k=2) = (3^2 * e^-3) / 2! ≈ 0.224

3. Final Answer:

   0.224 -> Option B

4. Quick Check:

   Poisson pmf(2,3) ≈ 0.224 [OK]

Hint: Use pmf(k) with mu to get exact event probability [OK]

Common Mistakes:

• Confusing pmf with cdf
• Rounding incorrectly
• Using wrong mu or k values

4. Identify the error in this code snippet:

from scipy.stats import poisson
rv = poisson(4)
prob = rv.pmf(3)
print(prob)

medium

A. poisson is not imported correctly

B. pmf cannot be called on rv object

C. No error, code runs correctly

D. The parameter should be named mu=4, not just 4

Solution

1. Step 1: Check the poisson object creation

   poisson(4) creates a frozen distribution with mean 4. The parameter can be passed positionally.

2. Step 2: Verify pmf method usage

   Calling pmf(3) on the frozen distribution is correct and prints the probability of 3 events.

3. Final Answer:

   No error, code runs correctly -> Option C

4. Quick Check:

   Frozen distribution with positional mu works = A [OK]

Hint: Frozen distribution accepts positional mu parameter [OK]

Common Mistakes:

• Thinking mu must be named explicitly
• Assuming pmf is not a method of frozen distribution
• Believing import is incorrect without error

5. You want to find the probability of observing at most 2 events when the average rate is 1.5. Which scipy code correctly calculates this?

hard

A. poisson.cdf(2, mu=1.5)

B. poisson.pmf(2, mu=1.5)

C. poisson.sf(2, mu=1.5)

D. poisson.cdf(1.5, mu=2)

Solution

1. Step 1: Understand the problem requirement

   We want the probability of at most 2 events, which means P(X ≤ 2).

2. Step 2: Identify the correct scipy function

   poisson.cdf(k, mu) gives P(X ≤ k). So poisson.cdf(2, mu=1.5) is correct.

3. Final Answer:

   poisson.cdf(2, mu=1.5) -> Option A

4. Quick Check:

   At most k events = cdf(k) [OK]

Hint: Use cdf(k) for probability of up to k events [OK]

Common Mistakes:

• Using pmf instead of cdf for cumulative probability
• Confusing survival function (sf) with cdf
• Swapping mu and k parameters