Probability Distribution Quiz

Some Special Distributions

•  Diskusi se distrik probabiliti blong ol sam spesel distribisen, olsem Binomial, Poisson, Gamma, Exponential, Chi-squared, Beta, mo Uniform.
•  Olgeta distribisen ia i save help long explain ol difren variabili blong ol jeneral fenomen.
•  Ol distrik ia i save folem difren paten.

Goals for this Chapter

•  Binomial mo ol distribisen we i save kamaot long en.
•  Poisson distribisen.
•  Distribisen blong Gamma, Exponential, Chi-squared, Beta, mo Uniform.
•  Normal distribisen.

Section 1: The Binomial and Related Distributions

•  Bernoulli experiment: One blong tu outcome (success/failure), we let p be probabiliti blong success every trial.
•  Example: male/female, or life or death, nondefective or defective.
•  Binomial distribution: A sequence blong independent and identical Bernoulli trials, where p (probability of success) i same long every trial. Olsem, number of success out of n trials.

Section 2: The Poisson Distribution

•  A good model for number of events that happen in space or time.
•  Probability of two events in very small increment of space or time is zero.
•  Useful for modeling number of events that occur per unit space or time.

Section 3: The Gamma, Exponential, Chi-squared, and Beta, Uniform Distributions

•  Ol sam spesel distribisen blong continuous random variables.
•  Ol jeneral fenomen na explain ol difren variabili blong ol skewed distributions, olsem time between failures or distance to shell impact.

Section 4: The Normal Distribution

•  Normal distribisen i save yus long explain very important phenomenon.
•  Natural phenomena save be normally distributed, olsem people height, IQ, wealth.
•  A special case use blong the Normal is a Standard Normal to get rid of any kind of variance.

Geometric Distribution

•  Independent trials, but only two outcomes are possible (success/failure).
•  X is the number of failures before the first success.
•  Number of trials before the first success.

Negative Binomial Distribution

•  Two outcomes only (success/failure).
•  Constant probability of success is p.
•  X is the number of failures until the rth success (r > 1).

Hypergeometric Distribution

•  Finite population.
•  Sampling without replacement.

Mean, Variance, and mgf of Distribution

•  Formula long calculate mean, variance, and moment generating functions (mgfs) blong every distribution.

Hemia wan quiz abaot probability distribution. Yu go long samting olsem geometric, negative binomial, poisson, mo beta functions. Findaem long ol question, wanem samting i faenem mo nao wanem i no faenem long ol specific distributions.