Probability Exam 2
Geometric (expected value and variance)
E[X] = 1/p Var(X) = (1 - p) / (p²)
Negative Binomial (expected value and variance)
E[X] = r/p Var(X) = r(1 - p) / (p²)
Poisson (expected value and variance)
E[X] = 𝝀 Var(X) = 𝝀
Bernoulli (expected value and variance)
E[x] = p Var(X) = p(1 - p)
Binomial (expected value and variance)
E[x]=np Var(x) = np(1 - p)
Poisson(𝝀)
𝝀 = np x = 0, 1, 2, ...
Binomial Random Variable
X denotes the *numbers of successes* in *n* independent trials where each trial has a probability of success of *p*
Bernoulli random variable
X denotes whether a trial that results in a success with probability *p* is a success or not
Geometric Random Variable
X is *numbers of trials needed* to obtain a success when each trial is independent with a probability of success of *p*
Hypergeometric Random Variable
X is defined to be the numbers of successes obtained in a *random sample, n* selected *without replacement* from a finite *population of N* elements that contains *m* successes and N-m failures
Negative Binomial Random Variable
X is numbers of trials needed to obtain to of *r* success when each trial is independent with a probability of success of p
Poisson Random Variable
X is used to denote the numbers of events that occur when these events are independent (or weakly dependent) and each have a small probability of occurrence
Binomial(n,p)
n = numbers of trials p = probability of success k = numbers of successful trails
Geometric(p)
p = probability of success k = first successful trial
Negative Binomial(r, p)
r = numbers of successes (failures) k = r, r + 1, r + 2, ...