math215 Lecture Notes - Lecture 4: Binomial Distribution, Poisson Distribution, Xu
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Assume x bin(n, : domain of variation : sx = {0, 1, . , n: probability mass function (pmf ) : p(x) =(cid:18)n, cumulative distribution function (cdf ) : F (x) = (where x denotes the integer part of x): expectation : x(cid:19) x(1 )n x, for x sx. X (where x denotes the integer part of x). Var(x) = : the uniform distribution, expectation , variance : Assume x u[ , : expectation , variance , domain of variation : sx = [ , , probability density function (pdf ) : f (x) , cumulative distribution function (cdf ) : 1 x for x sx for x sx. Assume x exp( : domain of variation : sx = [0, + , probability density function (pdf ) : f (x) = e x, cumulative distribution function (cdf ) : for x sx for x sx. 2: the normal distribution, expectation , variance :
