Geometric Distribution

What is the geometric distribution?

A distribution for the number of trials needed to get the first success in repeated independent trials (counts the trial with the success).

Write the notation used for the geometric distribution.

X ~ Geo(p), where X = number of trials up to and including the first success.

What are the 4 conditions for a geometric distribution?

Independent trials, each trial has two outcomes (success/failure), probability of success p is constant each trial, trials continue until first success/ aka unlimited trials, no upper bound

What is the mode of the geometric distribution?

Mode = 1 (most likely outcome is success on the first trial).

How do you calculate P(X = 3) for p = 0.2?

P(X=3) = (1−0.2)^(3−1) * 0.2 = 0.8^2 * 0.2 = 0.128.

How many trials do you expect on average until the first success if p = 0.25?

E(X) = 1 / 0.25 = 4 trials.