Bivariate Distributions: Binomial, Poisson, Normal - Definitions and Examples
Explore the definitions and examples of bivariate distributions including binomial, Poisson, and normal distributions. Understand the joint probability density functions, marginal distributions, and more in this comprehensive guide.
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Presentation Transcript
SOME SPECIAL SOME SPECIAL BIVARIATE DISTRIBUTIONS BIVARIATE DISTRIBUTIONS 11.2. Bivariate Binomial Distribution 11.2. Bivariate Binomial Distribution Definition 11.2 Definition 11.2. A discrete bivariate random variable (X, Y ) is said to have the bivariate binomial distribution with parameters n, p1, p2 if its joint probability density is of the form
Theorem that the marginal distributions of X and Y are BIN(n, p1) and BIN(n, p2), respectively. Theorem 11.4 11.4 Example: Example: if What is the p(X =5, Y=2) Answer Answer
11.6. Bivariate Poisson Distribution 11.6. Bivariate Poisson Distribution Definition 11.6. A discrete bivariate random variable (X, Y ) is said to have the bivariate Poisson distribution with parameters ?1, ? 2 , ? 3 if its joint probability density is of the form Definition 11.6.
12.5. Bivariate Normal Distribution 12.5. Bivariate Normal Distribution Definition 12.8 A continuous bivariate random variable (X, Y ) is said to have the bivariate normal distribution if its joint probability density function is of the form Definition 12.8. .
As usual, we denote this bivariate normal random variable by writing marginals of f(x, y) are given by
