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Binomial distribution provides a model for count data involving a fixed maximum

# Binomial distribution provides a model for count data involving a fixed maximum

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Binomial distribution provides a model for count data involving a fixed maximum. The features are a fixed number of independent trials with each one either being a success or a failure. The number of possible outcomes is given by 2^n. Formulas for binomial dist- (1) P(X=k) = (n,k) p^k (1-p)^n-k [where k is the number of successes and (n,k) is n!/k!(n-k)! (2) Excel- binomdist (k,n,p,0) for P(X=k) and binomdist(k,n,p,1) for P(X</ k) (3) Normal approximation where the mean is np and the sd is sqroot(npq). This is only valid if np and nq are both greater than or equal to 10. Poisson distribution provides a model for open end counts within a fixed interval. The mean is proportional to the size of the interval. The variance and mean are the same so the sd is the sqroot of the mean . Successive counts are independent between non- overlapping subunits. As the unit shrinks, the probability tends to be 0.

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Unformatted text preview: If X and Y are independent random variables then Z=X+Y with the means adding up. Formula for poisson dist-(1) P(X=k)= e^-u (u^k)/k ! [where e= 2.71828] (2) Excel- poissondist (k,u,0) for P(X=k) and poissondist(k,u,1) for P(X</k) Note if we need to get P(75 </ X </ 90) we do poissondist(90,84,1) – poissondist(74,84,1) and not 75. Conditional probability of B |A is the probability of an event B occurring given that A has definitely occurred. The general multiplication rule for this is P(A) X P(B |A). This is like multiplying across tree diagrams. (Extended version of this would be P(A and B and C)= P(A) X P(B |A) X P(C |A and B ). If A and B are independent then P(A |B)= P(A) since knowing B tells us nothing about the probability of A. Bayes rule- P(A |B)= P(A and B)/P(B). In other words, P(A |B)= P(A) x P(B |A)/P(A)xP(B |A) + P(Ac)xP(B |Ac)...
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Binomial distribution provides a model for count data involving a fixed maximum

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