Binomial distribution in SciPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the binomial distribution function from scipy.stats.

SciPy

from scipy.stats import [1]

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

Abinom

Bnorm

Cpoisson

Duniform

Attempts:

3 left

💡 Hint

Common Mistakes

Importing the normal distribution function instead of binomial.

Using a distribution unrelated to binomial like poisson or uniform.

The binom function in scipy.stats is used to work with the binomial distribution.

2fill in blank

medium

Complete the code to calculate the probability mass function (PMF) for 3 successes in 10 trials with success probability 0.5.

SciPy

prob = binom.pmf([1], 10, 0.5)

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

A3

B5

C7

D10

Attempts:

3 left

💡 Hint

Common Mistakes

Using the total number of trials instead of successes.

Confusing the order of arguments.

The PMF calculates the probability of exactly k successes. Here, k=3.

3fill in blank

hard

Fix the error in the code to calculate the cumulative distribution function (CDF) for 4 successes in 8 trials with probability 0.3.

SciPy

cdf_value = binom.[1](4, 8, 0.3)

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

Apdf

Bpmf

Ccdf

Dsf

Attempts:

3 left

💡 Hint

Common Mistakes

Using pmf or pdf instead of cdf.

Using survival function sf which is complementary.

The CDF function is cdf, which gives the probability of up to 4 successes.

4fill in blank

hard

Fill both blanks to create a dictionary of probabilities for successes greater than 2 in 5 trials with probability 0.4.

SciPy

prob_dict = {k: binom.[1](k, 5, 0.4) for k in range(3, [2])}

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

Apmf

Bcdf

C6

D5

Attempts:

3 left

💡 Hint

Common Mistakes

Using CDF instead of PMF for exact probabilities.

Using 5 as range upper bound which excludes 5.

We use pmf to get exact probabilities and range(3, 6) to include successes 3, 4, and 5.

5fill in blank

hard

Fill all three blanks to create a dictionary of probabilities for successes less than 4 in 7 trials with probability 0.6.

SciPy

probabilities = {k: binom.[1](k, [2], [3]) for k in range(4)}

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

Apmf

B7

C0.6

Dcdf

Attempts:

3 left

💡 Hint

Common Mistakes

Using CDF instead of PMF for exact values.

Mixing up number of trials or probability values.

We use pmf for exact probabilities, 7 trials, and 0.6 success probability.

Practice

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

easy

A. The relationship between two continuous variables

B. The number of successes in a fixed number of independent trials with the same success probability

C. The average value of a continuous variable

D. The total sum of all outcomes in a dataset

Solution

1. Step 1: Understand the binomial distribution concept

   The binomial distribution counts how many times an event happens in a fixed number of tries, where each try has the same chance of success.

2. Step 2: Match the description to the options

   The number of successes in a fixed number of independent trials with the same success probability correctly describes this as the number of successes in fixed independent trials with the same success chance.

3. Final Answer:

   The number of successes in a fixed number of independent trials with the same success probability -> Option B

4. Quick Check:

   Binomial distribution = count of successes [OK]

Hint: Binomial counts successes in fixed tries with same chance [OK]

Common Mistakes:

• Confusing binomial with normal distribution
• Thinking it models averages or sums
• Mixing up independent trials with dependent events

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

easy

A. import binom from scipy.stats

B. import scipy.binomial as binom

C. from scipy.stats import binom

D. from scipy import binomial

Solution

1. Step 1: Recall the correct import syntax for scipy.stats binomial

   The binomial distribution is accessed via scipy.stats as 'binom', so the correct import is 'from scipy.stats import binom'.

2. Step 2: Check each option's syntax

   from scipy.stats import binom matches the correct Python import syntax. Options A, B, and C are invalid Python import statements or incorrect module names.

3. Final Answer:

   from scipy.stats import binom -> Option C

4. Quick Check:

   Correct import = from scipy.stats import binom [OK]

Hint: Use 'from scipy.stats import binom' to import binomial [OK]

Common Mistakes:

• Using wrong module names like scipy.binomial
• Incorrect import syntax like 'import binom from ...'
• Forgetting to import from scipy.stats

3. What is the output of this code snippet?

from scipy.stats import binom
n, p = 5, 0.4
prob = binom.pmf(3, n, p)
print(round(prob, 3))

medium

A. 0.230

B. 0.345

C. 0.200

D. 0.410

Solution

1. Step 1: Understand binom.pmf parameters

   binom.pmf(k, n, p) gives the probability of exactly k successes in n trials with success chance p. Here, k=3, n=5, p=0.4.

2. Step 2: Calculate binomial probability for k=3

   Using the binomial formula or scipy, the probability is about 0.2304, rounded to 0.230.

3. Final Answer:

   0.230 -> Option A

4. Quick Check:

   binom.pmf(3,5,0.4) ≈ 0.230 [OK]

Hint: Use binom.pmf(k,n,p) for exact success probability [OK]

Common Mistakes:

• Confusing pmf with cdf
• Mixing up parameters order
• Rounding incorrectly

4. Identify the error in this code snippet:

from scipy.stats import binom
n, p = 10, 0.3
prob = binom.pmf(n, 10, p)
print(prob)

medium

A. The first argument to binom.pmf should be the number of successes, not total trials

B. The probability p should be an integer

C. The import statement is incorrect

D. The print statement is missing parentheses

Solution

1. Step 1: Check binom.pmf argument order

   binom.pmf(k, n, p) expects k = number of successes, n = number of trials, p = success probability.

2. Step 2: Analyze the code arguments

   Here, the first argument is n=10, which is total trials, not the number of successes. This is incorrect usage.

3. Final Answer:

   The first argument to binom.pmf should be the number of successes, not total trials -> Option A

4. Quick Check:

   binom.pmf(k,n,p) needs k successes first [OK]

Hint: First arg to pmf is successes, not total trials [OK]

Common Mistakes:

• Swapping k and n arguments
• Using integer for probability p
• Incorrect import or print syntax

5. You want to find the probability of getting at most 2 successes in 8 trials with success chance 0.5 using scipy. Which code snippet correctly calculates this cumulative probability?

hard

A. binom.cdf(8, 2, 0.5)

B. binom.pmf(2, 8, 0.5)

C. binom.sf(2, 8, 0.5)

D. binom.cdf(2, 8, 0.5)

Solution

1. Step 1: Understand cumulative probability for 'at most' successes

   To find probability of at most 2 successes, use cumulative distribution function (cdf) up to 2.

2. Step 2: Match correct function and parameters

   binom.cdf(2, 8, 0.5) correctly computes P(X ≤ 2) for n=8, p=0.5. Other options either use pmf (exact), sf (survival function), or wrong parameter order.

3. Final Answer:

   binom.cdf(2, 8, 0.5) -> Option D

4. Quick Check:

   Use binom.cdf(k,n,p) for P(X ≤ k) [OK]

Hint: Use binom.cdf for cumulative probability up to k [OK]

Common Mistakes:

• Using pmf instead of cdf for cumulative
• Swapping n and k parameters
• Using survival function sf for 'at most' instead of 'more than'