Calculating Parameters for a Geometric Distribution

These flashcards cover key concepts related to the geometric distribution, including parameters, calculations, and the relevant probability functions.

Geometric Distribution

A statistical distribution of a number of trials until the first success occurs in a series of independent Bernoulli trials.

Mean (μ)

In a geometric distribution, the mean is calculated as μ = 1/P, where P is the probability of success.

Standard Deviation (σ)

In a geometric distribution, the standard deviation is calculated as σ = squareroot(q/p²), where q = 1 - p and P is the probability of success.

Probability of Success (p)

The likelihood of achieving a success in a single trial.

Probability of Failure (q)

The likelihood of failing in a single trial, calculated as q = 1 - p.

10% Rule

A condition stating it is acceptable to use the geometric model as long as fewer than 10% of the population is sampled, ensuring independence of trials.

Geometric Probability Function

The function for finding the probability of the first success on the x-th trial, given by P(X = x) = q^(x-1) * p.

Independent Trials

Trials that do not influence each other's outcomes, each having the same probability of success.

Parametric Calculation

Using specific mathematical formulas to derive mean and standard deviation for geometric distributions.

Example Calculation of Geometric Probability: If Jeremiah makes 25% of three-point shots, the probability he makes his first successful shot on his 3rd attempt is calculated as?

his 3rd attempt is calculated as P(M=3) = (0.75)² * (0.25) = 0.14.