# Hypergeom_to_categ Flashcards

What is the Hypergeometric distribution, and how is it commonly used in data analysis and machine learning?

The Hypergeometric distribution describes the number of successes in a sample drawn from a finite population without replacement. It’s used when calculating the probability of obtaining specific successes in a sample without returning items to the population. In data analysis and machine learning, it’s useful for scenarios like assessing sample quality or validating model performance using limited data.

Could you explain the Probability Mass Function (PMF) of the Hypergeometric distribution and its formula?

The Hypergeometric PMF calculates the probability of getting exactly k successes in a sample of size n. Formula: P(X=k)=(nN)(kK)⋅(n−kN−K)

How does the Cumulative Distribution Function (CDF) of the Hypergeometric distribution differ from the PMF, and what does it represent?

The Hypergeometric CDF gives the probability of getting k or fewer successes in a sample of size n. Formula: P(X≤k)=∑i=0kP(X=i)

Can you provide an example that illustrates the Hypergeometric distribution?

Imagine you have a batch of 1000 items, with 150 defective ones. If you randomly select 20 items, what’s the probability of getting exactly 3 defective items?

How do you calculate the probability of getting 3 defective items in the given example using the Hypergeometric distribution?

Using the Hypergeometric PMF formula and calculating binomial coefficients: P(X=3)=(201000)(3150)⋅(20−31000−150)

How can understanding the Hypergeometric distribution be valuable in data engineering or machine learning?

In data engineering, it’s useful for assessing sample quality or validating data subsets. In machine learning, it helps estimate the likelihood of observing specific outcomes in model evaluations, especially with limited data.

What is the Negative Binomial distribution, and how does it differ from the Geometric distribution?

The Negative Binomial distribution models the trials needed for r successes in independent Bernoulli trials. Unlike the Geometric distribution, it considers total trials for r successes, not just the first success.

Could you explain the Probability Mass Function (PMF) of the Negative Binomial distribution and its formula?

Negative Binomial PMF gives r successes on k-th trial. Formula: P(X=k)=(r−1k−1)⋅pr⋅(1−p)k−r

How does the Cumulative Distribution Function (CDF) of the Negative Binomial distribution differ from the PMF, and what does it represent?

Negative Binomial CDF gives prob. of k or fewer trials for r successes. Formula: P(X≤k)=∑i=rkP(X=i)

Can you provide an example that illustrates the Negative Binomial distribution?

Imagine flipping a biased coin until 5 heads. Each flip has 0.3 chance of heads. What’s the prob. of taking 10 flips for 5 heads?

How do you calculate the probability of getting 5 heads on the 10th flip in the given example using the Negative Binomial distribution?

Using Negative Binomial PMF: P(X=10)=(5−110−1)⋅0.35⋅(1−0.3)10−5

How can understanding the Negative Binomial distribution be valuable in data engineering or machine learning?

It models attempts needed for a specific success count, like conversions. In ML, it might estimate iterations for training to reach a performance level.

What is the Discrete Uniform distribution, and when do we commonly encounter it?

The Discrete Uniform distribution is a probability distribution where all outcomes are equally likely within a finite set of values. It’s encountered in scenarios where each outcome has the same probability, without any bias towards specific values.

Could you explain the Probability Mass Function (PMF) of the Discrete Uniform distribution and its formula?

The Discrete Uniform PMF assigns an equal probability to each possible outcome. Formula: P(X=x)=n1 where X is the outcome, x is a specific value, and n is the total number of outcomes.

How does the Cumulative Distribution Function (CDF) of the Discrete Uniform distribution work?

The Discrete Uniform CDF gives the probability that the outcome is less than or equal to a specific value. It’s a step function increasing by n1 at each outcome.