Poisson distribution in SciPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the Poisson distribution from scipy.stats.

SciPy

from scipy.stats import [1]

Drag options to blanks, or click blank then click option'

Apoisson

Bbinom

Cnorm

Duniform

Attempts:

3 left

💡 Hint

Common Mistakes

Importing the normal distribution instead of Poisson.

Using a distribution for continuous data instead of discrete.

The Poisson distribution is available as poisson in scipy.stats.

2fill in blank

medium

Complete the code to calculate the probability of exactly 3 events when the average rate is 2.

SciPy

prob = poisson.pmf([1], mu=2)

Drag options to blanks, or click blank then click option'

A2

B1

C0

D3

Attempts:

3 left

💡 Hint

Common Mistakes

Using the mean value instead of the event count as the first argument.

Confusing pmf with cdf.

The pmf function calculates the probability of exactly k events. Here, k=3.

3fill in blank

hard

Fix the error in the code to calculate the cumulative probability of up to 4 events with mean 3.

SciPy

cum_prob = poisson.[1](4, mu=3)

Drag options to blanks, or click blank then click option'

Apmf

Bcdf

Cpdf

Dsf

Attempts:

3 left

💡 Hint

Common Mistakes

Using pmf which gives probability of exactly k events.

Using sf which gives the survival function (1 - cdf).

The cdf function calculates the cumulative probability up to a given number of events.

4fill in blank

hard

Fill both blanks to create a dictionary of probabilities for 0 to 5 events with mean 2.

SciPy

prob_dict = {k: poisson.[1](k, mu=[2]) for k in range(6)}

Drag options to blanks, or click blank then click option'

Apmf

Bcdf

C2

D3

Attempts:

3 left

💡 Hint

Common Mistakes

Using cdf instead of pmf for exact probabilities.

Using wrong mean value.

Use pmf to get exact probabilities and mean 2 as given.

5fill in blank

hard

Fill all three blanks to filter events with probability greater than 0.1 from a dictionary.

SciPy

filtered = {k: v for k, v in prob_dict.items() if v [1] [2]
threshold = [3]

Drag options to blanks, or click blank then click option'

A>

B0.1

C<

D0.05

Attempts:

3 left

💡 Hint

Common Mistakes

Using less than instead of greater than.

Using wrong threshold value.

We filter probabilities greater than 0.1, so use > and 0.1 as threshold.

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