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ckn.m function y = ckn(P,k) determines the probability of the occurrence of k or more of the n independent events whose probabilities are in row or column vector P ( k may be a row or column vector)

function y = ckn(P,k) % CKN y = ckn(P,k) Probability of k or more successes% Version of 5/15/95 % Probabilities of k or more of n independent events% Uses the m-functions mintable, minprob, csort n = length(P);m = length(k); T = sum(mintable(n)); % The number of successes in each mintermpm = minprob(P); % The probability of each minterm [t,p]= csort(T,pm); % Sorts and consolidates success numbers % and adds corresponding probabilitiesfor i = 1:m % Sums probabilities for each k value y(i) = sum(p(k(i)+1:n+1));end
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parallel.m function y = parallel(p) determines the probability of a parallel combination of the independent events whose probabilities are in row or columnvector p .

function y = parallel(p) % PARALLEL y = parallel(p) Probaaability of parallel combination% Version of 3/3/93 % Probability of parallel combination.% Individual probabilities in row matrix p. y = 1 - prod(1 - p);
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Conditional probability and conditional idependence

bayes.m produces a Bayesian reversal of conditional probabilities. The input consists of P ( E | A i ) and P ( A i ) for a disjoint class { A i : 1 i n } whose union contains E . The procedure calculates P ( A i | E ) and P ( A i | E c ) for 1 i n .

% BAYES file bayes.m Bayesian reversal of conditional probabilities % Version of 7/6/93% Input P(E|Ai) and P(Ai) % Calculates P(Ai|E) and P(Ai|Ec)disp('Requires input PEA = [P(E|A1) P(E|A2) ... P(E|An)]')disp(' and PA = [P(A1) P(A2) ... P(An)]')disp('Determines PAE = [P(A1|E) P(A2|E) ... P(An|E)]')disp(' and PAEc = [P(A1|Ec) P(A2|Ec) ... P(An|Ec)]')PEA = input('Enter matrix PEA of conditional probabilities '); PA = input('Enter matrix PA of probabilities ');PE = PEA*PA'; PAE = (PEA.*PA)/PE;PAEc = ((1 - PEA).*PA)/(1 - PE); disp(' ')disp(['P(E) = ',num2str(PE),])disp(' ') disp(' P(E|Ai) P(Ai) P(Ai|E) P(Ai|Ec)')disp([PEA; PA; PAE; PAEc]')disp('Various quantities are in the matrices PEA, PA, PAE, PAEc, named above')
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odds.m The procedure calculates posterior odds for for a specified profile E . Assumes data have been entered by the procedure oddsf or oddsp .

% ODDS file odds.m Posterior odds for profile % Version of 12/4/93% Calculates posterior odds for profile E % Assumes data has been entered by oddsdf or oddsdpE = input('Enter profile matrix E '); C = diag(a(:,E))'; % aa = a(:,E) is an n by n matrix whose ith columnD = diag(b(:,E))'; % is the E(i)th column of a. The elements on the % diagonal are b(i, E(i)), 1<= i<= n % Similarly for b(:,E)R = prod(C./D)*(p1/p2); % Calculates posterior odds for profile disp(' ')disp(['Odds favoring Group 1: ',num2str(R),])if R>1 disp('Classify in Group 1')else disp('Classify in Group 2')end
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Source:  OpenStax, Applied probability. OpenStax CNX. Aug 31, 2009 Download for free at http://cnx.org/content/col10708/1.6
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