Sommario corso statistics

REVIEW POISSON APPROXIMATION

PROBABILITY TABLE table where we have 2 variables (X, Y), with joint

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probabilities inside and marginal probabilities on the right/bottom.

Properties:

Each joint probability greater or equal than 0 and less or equal than 1

 Sum of all joint probabilities equal to 1

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Marginal probability:

P(x) = sum of all joint probabilities of y keeping x fixed

 P(y) = sum of all joint probabilities of x keeping y fixed

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4 possible conditional probabilities:

1. P(X|Y=0) conditional mean = X1*P(X1|Y0)+X2*P(X2|Y0) P(X2|Y0) + 1

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2. P(X|Y=1) conditional mean = X1*P(X1|Y1)+X2*P(X2|Y1) P(X2|Y1) + 1

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3. P(Y|X=1) conditional mean = Y0*P(Y0|X1)+Y1*P(Y1|X1) P(Y1|X1)

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4. P(Y|X=2) conditional mean = Y0*P(Y0|X2)+Y1*P(Y1|X2) P(Y1|X2)

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Conditional variance:

Normal sum(y-mean)^2*P(y|x)

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Bernoulli o^2(Y|X) = P(Y0|X)*P(Y1|X) or o^2(X|Y) = P(X1|Y)*P(X2|Y)

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