Interview Q&A / Data Science

1. How does Bayes theorem work? Explain with a medical test example.

   Bayes theorem updates a probability using new evidence: P(A|B) = P(B|A) x P(A) / P(B). It shows that a positive result from an accurate test can still mean a low chance of disease when the disease is rare.

   IntermediateQuick answer1 min read
2. What does the exponential distribution model?

   The exponential distribution models the waiting time until the next event when events arrive randomly at a constant rate. It is memoryless: the time already waited does not change the remaining wait.

   IntermediateQuick answer1 min read
3. What is the birthday paradox?

   In a group of just 23 people, the chance that two share a birthday is about 51%. It feels surprising because the number of pairs grows fast: 23 people form 253 pairs, each a chance for a match.

   IntermediateQuick answer1 min read
4. What is the difference between the Law of Large Numbers and the Central Limit Theorem?

   The Law of Large Numbers says the sample mean converges to the true mean as n grows. The Central Limit Theorem describes the shape and spread of the sample mean around that true value: approximately normal with SD sigma over root n.

   IntermediateQuick answer1 min read
5. What is the Poisson distribution, and what kind of data does it model?

   Poisson models the number of events in a fixed interval of time or space when events occur independently at a constant average rate. It has one parameter, the rate lambda, which is both its mean and its variance.

   IntermediateQuick answer1 min read