Geometric distributions are always skewed right because the probability of success decreases with each trial.

The mean (expected value) represents the average number of trials needed to achieve the first success.

Standard deviation measures how much the number of trials typically varies from the mean number of trials until the first success.

The expected value is the inverse of the probability of success on each trial.

Each trial is independent, meaning the outcome of one trial does not affect the outcome of any other trial.

$P(Y = k) = (1-p)^{k-1} * p$

$E(Y) = \frac{1}{p}$

$σ_Y = \sqrt{\frac{1-p}{p^2}}$

E(Y) = 1/0.4 = 2.5

$σ_Y = \sqrt{\frac{1-0.5}{0.5^2}} = 1$

Counts the number of trials needed to get the first success in a series of independent trials.

One of two possible outcomes in each independent trial, with a fixed probability p.

The other possible outcome (besides success) in each independent trial, with a probability of 1-p.

The probability of the first success occurring on the kth trial.

Probability of the first success on or before trial k (cumulative probability).