Chapter 3 (Discrete Probability Distributions) Flashcards
What are the rules for a Binomial Distribution?
1) Fixed # of trials (n)
2) Each trial results in success or failure
3) Each trial is independent
4) The probability (p) is fixed (aka the same) for each trial
5) X (the r.v.) counts the number of successes.
What kind of random variable is used in the binomial distribution?
Discrete random variable!
What is the pmf for a binomial distribution?
P(X=x) = (“n”choose “x”)p^x(1-p)^{n-x}
(“n”choose”x”) - how many ways we can observe x successes out of n trials.
p^x = number of successes we will observe
(1-p)^{n-x} = number of failures we will observe.
How is a binomial distribution notated?
X~Binomial(n,p)
n = # of trials
p = probability
What are the rules for a Poisson Distribution?
1) There is an amount of time
2) X (the r.v.) counts the times something occurs in that amount of time.
3) We consider the mean (mu) of X.
What kind of random variable is used in the Poisson Distribution?
Discrete random variable!
What is the pmf for a Poisson distribution?
P(X=x) = (mu^x)(e^-mu)
————————–
x!
How is a Poisson Distribution notated?
X~Poisson(myu)
myu = the mean!
What are the rules for a Geometric Distribution?
1) X counts the # of trials until the 1st success.
2) Every trial will result in success of failure.
3) The probability is the same for each trial.
4) All trials are independent.
What kind of random variable is used in the Geometric Distribution?
Discrete Random Variable!
What is the pmf for a Geometric Distribution?
P(X=x) = [(1-p)^{x-1}] * p
What is E(X) for a geometric distribution?
E(X) = 1/p
What is the Var(X) for a geometric distribution?
Var(X) = (1-p)/p^2
What is E(X) for a Poisson Distribution?
E(X) = mu
What is Var(X) for a Poisson Distribution?
Var(X) = mu
