Comprehensive statistics interview questions covering probability, distributions, hypothesis testing, and statistical analysis.

Easy-level statistics interview questions covering fundamental concepts, descriptive statistics, and basic probability. Q1: Explain the difference between mean, median, and mode. Answer: Definitions Mean ($\bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i$): Arithmetic average of all values Median: Middle value when data is …

Visual guide to Bayesian reasoning and updating beliefs with evidence. Formula $$ P(H|E) = \frac{P(E|H) \cdot P(H)}{P(E)} $$ $P(H|E)$: Posterior (probability of hypothesis given evidence) $P(E|H)$: Likelihood (probability of evidence given hypothesis) $P(H)$: Prior (initial probability of hypothesis) $P(E)$: Marginal …

Visual demonstration of the Central Limit Theorem - why averages are normally distributed. Statement The sum (or average) of many independent random variables tends toward a normal distribution, regardless of the original distribution. $$ \frac{\bar{X} - \mu}{\sigma/\sqrt{n}} \xrightarrow{d} N(0, 1) \quad \text{as } n …

Visual guide to common probability distributions with their properties and use cases. Normal (Gaussian) Distribution Symmetric bell curve - most common distribution in nature. $$ f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{2\sigma^2}} $$ Mean: $\mu$ Variance: $\sigma^2$ Symmetric around mean 68-95-99.7 rule …

Interactive visualization of Monte Carlo methods for solving complex problems through random sampling. Principle Use random sampling to solve deterministic or stochastic problems. Estimating π - Interactive Animation Integration Concept Monte Carlo integration works by randomly sampling points and determining the ratio …

Visual guide to probability fundamentals and axioms. Axioms of Probability Axiom 1: Non-Negativity $$0 \leq P(A) \leq 1 \text{ for any event } A$$ Probabilities are always between 0 (impossible) and 1 (certain). Axiom 1: Probability Range [0, 1] 0.0 Impossible 0.5 Equally Likely 1.0 Certain Impossible Unlikely (0.25) …

Expected Value $$ E[X] = \sum_x x \cdot P(X=x) \quad \text{(discrete)} $$ $$ E[X] = \int_{-\infty}^{\infty} x \cdot f(x) dx \quad \text{(continuous)} $$ Variance $$ \text{Var}(X) = E[(X - E[X])^2] = E[X^2] - (E[X])^2 $$ Python 1import numpy as np 2 3data = np.random.normal(0, 1, 10000) 4 5mean = np.mean(data) 6variance …

Essential concepts and applications of statistics, probabilities, including distributions, Bayesian inference, and Monte Carlo methods.