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Probability Exam 2
UIUC Math 461 Stat 400 Exam 2 Distribution Independence
6
Mathematics
Undergraduate 3
04/03/2014

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Cards

Term
Geometric Distribution
Definition
# of bernouli trials to get one success

p.m.f= (1-p)^(k-1)*(p)

var=(1-p)/(p^2)
Term
Binomial Distribution
Definition
p=prob in n=trials, usually finding probability of getting some X<=n p.m.f= (n choose k)(p^k)(1-p)^(n-k)

var=np(1-p)
Term
Poisson
Definition
given lambda

expected value=lambda L
var=lambda

P(X=k)=(e^-L)((L^k)/(k!))
Term
Bayes Theorem
Definition
P(X|Y)=P(X given Y)=((P(Y|X)*P(X))/(P(Y|X)*P(X)-P(Y|Xc)*P(Xc))
Term
var[x]
Definition
E[x^2]-E[x]^2
Term
P(X>n) Geometric
Definition
(1-p)^n

this is obvious though. think about it. the first success has to be greater than n if and only if there are at least n failures in a row first.
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