Geometric distribution

Understanding the Concept “Geometric Distribution”

• The geometric distribution is a kind of probability distribution that is often used in statistical modelling.
• It refers to the probability distribution of the number of trials required to get the first success in repeated Bernoulli trials.
• Each Bernoulli trial is independent of others and carries the same probability of success.

Key Properties of Geometric Distribution

• Memorylessness: The chance of success on the next trial is always the same, regardless of past failures.
• Geometric distribution is used in problems where the time until some specific event occurs for the first time is being measured.
• If ‘p’ is the probability of success, and ‘q’ is the probability of failure (q = 1 – p), the probability mass function of geometric distribution is represented by P(X=x) = q^(x-1) * p, where ‘x’ is the number of trials required for the first success.

Applying Geometric Distribution

• Geometric distribution is employed in a wide array of real-life contexts such as engineering, finance, and medical research.
• Practical instances could include situations like finding the number of coin tosses before obtaining the first head, or gauging how many times a salesperson has to call potential clients before making the first sale.

Key Points to Keep in Mind

• While working with geometric distribution, it is important to clarify whether the number of trials ‘X’ includes the successful trial or not.
• The expected value or mean of a geometric distribution with success probability ‘p’ is 1/p.
• The variance, or measure of how spread out the numbers in the data are, of a geometric distribution with success probability ‘p’ is (1-p)/p².
• Understanding the characteristics of geometric distribution can help in making more accurate and informed decisions in various fields.