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Binomial Random Variable

A random variable that counts the number of successes in a fixed number of independent trials, where each trial has two possible outcomes.

Geometric Random Variable

A random variable that counts the number of trials until the first success occurs.

Conditions for Binomial Distribution

There must be a fixed number of trials, the trials must be independent, there must be only two outcomes, and the probability of success must be constant.

Mean of Binomial Distribution

The expected number of successes, calculated as $\text{mean} = n \times p$ where $n$ is the number of trials and $p$ is the probability of success.

Standard Deviation of Binomial Distribution

A measure of spread in the number of successes, calculated as $\text{SD} = \text{sqrt}(n \times p \times (1-p))$.

Normal Approximation to Binomial Distribution

When the sample size is large enough, the binomial distribution can be approximated by a normal distribution if both expected successes and failures are at least 10.

Population Parameter vs. Sample Statistic

A parameter describes a whole population while a statistic describes a sample drawn from that population.

Sampling Distribution

The distribution of a statistic (like the mean) calculated from all possible samples of a given size from a population.

Unbiased Estimator

A statistic that is expected to equal the true parameter value on average.

Margin of Error

The range of values above and below the sample statistic in a confidence interval, reflecting the uncertainty of the estimate.

Point Estimate

A single value given as the estimate of a population parameter.

Confidence Interval

A range of values derived from the sample statistic that is likely to contain the true population parameter.

Type I Error

A false positive; rejecting a true null hypothesis.

Type II Error

A false negative; failing to reject a false null hypothesis.

Expected Counts (Chi-Square Test)

The counts that are expected in each category under the null hypothesis.