Binomial Distribution
This page delves into the binomial distribution, a crucial concept in probability theory and statistics.
Definition: The binomial distribution models the number of successes in a fixed number of independent trials, each with the same probability of success.
The binomial distribution is characterized by two parameters:
- n: the number of trials
- p: the probability of success on each trial
Vocabulary: An experiment with only two possible outcomes (success or failure) is called a Bernoulli trial.
The probability mass function for a binomial distribution X ~ B(n,p) is:
P(X = k) = (n choose k) × p^k × (1-p)^(n-k)
Where:
- k is the number of successes
- (n choose k) is the binomial coefficient
Example: In a series of 10 coin flips (n = 10) with a fair coin (p = 0.5), the probability of getting exactly 3 heads can be calculated using the binomial distribution formula.
Key properties of the binomial distribution include:
- Expected value: E(X) = np
- Variance: V(X) = np(1-p)
- Standard deviation: σ(X) = √(np(1-p))
Highlight: The binomial distribution is widely used in various fields, including quality control, epidemiology, and finance, making it a crucial topic in Loi binomiale - Terminale courses.
Understanding the binomial distribution is essential for solving problems involving repeated independent trials with fixed probabilities, which are common in many Loi binomiale exercices corrigés PDF resources.
