Earth Stats Week #2 Readings

A set of vocabulary flashcards based on the lecture notes covering key statistical concepts, probability distributions, confidence intervals, and standard error.

Normal Distribution

A bell-shaped, symmetric, continuous distribution defined over all real numbers by two parameters: mean ($\mu$) and variance ($\sigma^2$), where $\sigma$ is the standard deviation.

Central Limit Theorem

The principle stating that the average of many independent samples with finite mean and variance converges to a normal distribution as the sample size grows.

Binomial Distribution

A discrete distribution modeling the number of successes in a fixed number of independent trials ($n$), each with two outcomes and a constant success probability ($p$), having a mean of $n \cdot p$ and variance of $n \cdot p \cdot (1-p)$.

Bernoulli Trials

A single experiment with exactly two outcomes, where success occurs with probability $p$ and failure with probability $1-p$, serving as the building block of the binomial distribution.

Confidence Interval

A range of values likely to contain a true population parameter, defined such that if the sampling process is repeated many times, a stated percentage (e.g., $95\%$) of resulting intervals will contain the true parameter.

Bayesian Credible Interval

An interval structure to which the interpretation that there is a $95\%$ probability the true population parameter lies in that specific interval correctly belongs.

Standard Error

The standard deviation of a statistic's sampling distribution, rather than of raw data, which is used in constructing confidence intervals.

Standard Error of the Mean

A metric computed as standard deviation $\div \sqrt{\text{sample size}}$, where larger sample sizes produce smaller standard errors.