Unformatted text preview: Chapter 1: Descriptive Statistics Sample Average Population Average
_ N
f2§23=1mi #:%Z,—:1ri 82 _n:12($i E)2_n:1(2wf (21:31)) Pk: —E Chebychev’s Rule: The proportion of observations that are within 3:: standard
1 deviations (pk) of the mean is at least: hapter 2: Probability Multiplication rule Permutation Combination For anv two events A and B:
_ P(A U B) :P(A)+P(B) — P{A n B) n1 xngxnz...xnk Pkﬁzﬁ Two events A and B are independent if conditional probability of A given
that B occurred [P(B) > 0): P(AB) = P(A) HA and B are independent then Chapter 3:Discrete PDF
E(aX + b) : cE(X) +b
V(a.X + b) = cﬂ/(X) = azai’
3.1 Binomial Distribution
For X N binomial“;J p} n : ﬁxed number of trials p : probability of succes (S) :r : number of successes (S) Tl.
P(X =3)=(m)pz(1,p)n—=
:r:0,1,2,...,n PA B
PtAnBJ:P(A)P(B) PWBJ=% n=ElX1 =71? 2=Vle=EH$—#)21=HP(1—P . If A, B, C, D, . . . are mutually independent then
P(AﬂB N Go D. . .) : P(A)P(B)P(C)P(D) . . 3.2 Multinomial Distribution
For X N multinomial(n,p1, . . . ,pr)
11 = Number of trials. 5“ = Number of possible outcomes. .6 Negative Binomial Probability Distribution
 or X N negative binomial[r,p}
'r : number of S
p = probability of S Em = a
vmp:ﬁ _ rﬂP) P
, rﬂP)
7 P2 a: = the number of failures preceding the r‘th success If 'r = 1 we have a Geometric distribution.
3.7 Poisson Distribution E[X] = ,u = A For X N poissonOi) vmp=ﬂ=i A = the rate per unit time or rate per unit area. m = the number of successes occurring during
a given time interval or in a speciﬁed region When n _’ 00 and P _' 0 and A 2 up Pg=m= e‘AAz 9:! $20,1,2,... A>0 3.8 Poisson Approximation to the
Binomial Distribution Let X be a binomial random variable with
probability distribution X m binomialm, p). remains ﬁxed at A > D, then X N binomial[n,p) —> X N poisson()\ 2 up” pg : P(Outcome 2‘ on any particular trial).
m: = Number of trials resulting in outcome 2‘. n! p(ml‘l $27 ' ' ' 7 $1") : Ellﬂigl...
m1+2¢2+...:r,=r azanam m, masks r
1" ...
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 Spring '07
 Parzen

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