InterviewSkill
Probability fundamentals for data, ML, statistics, experimentation, and analytical interview rounds.
Conditional probability is the probability of an event given that another event has already occurred.
It is written as P(A | B) and calculated as P(A and B) / P(B), when P(B) is not zero. It helps reason about updated information in experiments, diagnostics, and ML classification.
Bayes' theorem updates the probability of a hypothesis using prior belief and observed evidence.
It is commonly written as P(A | B) = P(B | A)P(A) / P(B). In interviews, it is useful for medical tests, spam detection, fraud detection, and model reasoning under uncertainty.
Two events are independent if knowing one happened does not change the probability of the other.
For independent events A and B, P(A and B) = P(A)P(B), and P(A | B) = P(A). Independence is stronger than simply being different events.
A random variable maps outcomes of a random process to numeric values.
Random variables can be discrete, like the number of clicks, or continuous, like response time. They let us describe uncertainty with distributions, expectation, and variance.
Expected value is the long-run average value of a random variable.
For a discrete random variable, it is the sum of each value times its probability. It is useful for decision-making, risk analysis, ranking, and evaluating bets or product outcomes.
Variance measures how spread out values are around the mean.
A higher variance means outcomes are more dispersed and less predictable. Standard deviation is the square root of variance and is easier to interpret because it uses the original units.
Use Bernoulli for one binary trial, binomial for the number of successes across fixed trials, and normal for many continuous measurements or approximations.
These distributions model different kinds of uncertainty. Interviewers often expect you to connect the distribution to the data-generating process rather than memorize formulas.
The law of large numbers says that sample averages tend to get closer to the expected value as sample size grows.
It explains why more data usually gives more stable estimates. It does not guarantee every small sample is accurate, and it does not remove bias from a bad sampling process.