Geometric Distribution Vocabulary

Flashcards covering key definitions, formulas, and rules for Geometric Distribution based on lecture notes.

Geometric Distribution

A discrete probability distribution that models the number of repeated independent trials required until success occurs for the first time.

Probability Function $P(X = r)$

The formula to find the probability that the first success occurs on trial $r$, given by $P(X = r) = q^{r-1}p$.

Cumulative Probability $P(X \le r)$

The probability that the first success occurs on or before trial $r$, calculated as $P(X \le r) = 1 - q^r$.

Tail Probability $P(X > r)$

The probability that more than $r$ trials are needed to achieve the first success, calculated as $P(X > r) = q^r$.

Expected Value / Mean

The average number of trials required to obtain the first success in a geometric distribution, given by $\text{Expected Value / Mean} = \frac{1}{p}$.

Success Probability ($p$)

The constant probability of obtaining a successful outcome in each independent trial.

Failure Probability ($q$)

The constant probability of obtaining a failure in each independent trial, defined as $q = 1 - p$.

Inequality Conversion for $P(X < r)$

The strict inequality $P(X < r)$ converts to the cumulative probability $P(X \le r - 1) = 1 - q^{r-1}$.

Inequality Conversion for $P(X \ge r)$

The weak inequality $P(X \ge r)$ converts to the tail probability $P(X > r - 1) = q^{r-1}$.