Risk and uncertainty - formule

Replacement finite discrete models with equally likely outcomes

Pr(E) = number of outcomes in event E = r = n(E) M. r objects into n urns total number of possible outcomes n n(S)

• Multiplication: n(A) n(B) (ex. License plates, wardrobe)

Me ⑨. Order

P = n!

Permutation: n r A. n objects chosen r at a time (n - r)!

Combination: C = n! = nn rM n objects chosen r at a time ASEEr! (n - r)! r

Operations summary

n nn r n-r

• Multiplications: when there is “and”, choose multiple things A B (elements in both)

Binomial theorem = (x+y) = ∩x y Mr .M

• Plus: when there is “or”, choose either one or the other A B (elements in common)∪M.
• Subtraction: get rid of some cases

Conditional probability

• Division: when you are counting something more times than needed (especially with sets)

Representation

In order to find the conditional probability Pr(A∩B)=B)Pr(AM• Pr(B). See Bayesian theorem

In order to find Pr(A∩B): Morgan’s laws Pr(A∩B) = P(A B) P(B)M (A B) = A B∩ ∪

In order to find Pr(B): (A B) = A B∪ ∩ P(B) = Pr(A∩B) + Pr(A ∩B)M,

Bayesian formula: causes precedes effect multiply B Pr(A B C) = Pr(A B C)Pr(B C)Pr(C). - ∩ ∩ ∩M-

Pr(A B) = P r(A∩B) = Pr(A)⋅Pr(B A) 'B• .Pr(A∩B) + Pr(A∩B) Pr(A)⋅Pr(B A)+Pr(A)⋅Pr(B A)1I i B use percentile' y odd: middle value Bsum where you find B ‣ formula (with 50%)*

Baye’s theorem median

Even: sum of the 2 middle value divided by 2‣)BPr(A·)Pr(B=)BPr(A·)Pr(B=Pr(B=A)Pr(B ∩A) ‣kkkkkkM nPr(A) )BPr(A·)Pr(BPr(A) minimum + maximumii midrangei = 1 ‣‣)Pr(A∩B 2i✓

Discrete random variables

Measures of support probability most frequent value mode ⑧‣‣P(X=x)=p(x) = F(x)= P(X<x)

Central tendency

With probability function ‣/probability distribution cumulative distribution = E(X) = x · p(x )‣with µ deals. .← i i mean or expected value ( ) X .µ = E(g(x)) = g(x · p(x ))µσ i iX2 22 ‣ variance .V(X) = = E(X ) - (E(X))