STAB22H3 Chapter Notes - Chapter 15: Bayes Estimator

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25 Apr 2013

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STAB22H3 Full Course Notes

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Conditional probability probability that takes into account a given condition. When we want the probability of an event from a conditional distribution, we write p(b|a) and say the probability of b given a : p(b|a) = p(a and b)/p(a) The formula does not work if p(a) = 0. Dependent events p(b|a) p(b|ac), the probability of b is not the same conditional on a as it is conditional on ac. Independent events - p(b|a) = p(b|ac) = p(b), the probability of b is the same conditional on a as it is conditional on ac. Events a and b are independent if and only if the probability of b is the same when we are given that a has occurred p(b) = p(b|a) P(a and b) = p(a) x p(b|a) The probability that two events, a and b both occur is the probability that a occurs multiplied by the probability that b occurs (given that a occurs)

Related Questions

You are given a fair die, i.e. the outcomes of any throw are contained in the sample space Let the event A be that an even number is thrown and the event B that a multiple of three is thrown. Now consider the two random variables X and Y. X takes on a value of 1 if the event A has occurred and the value 0 if A has not occurred. The random variable Y takes on the value of 1 if the event B has occurred and the value zero if B has not occurred.

(a) Derive the joint pdf of X and Y. Provide this in the form of a table

Y=0 Y=1

X=0
X=1

b) What is the marginal probability distribution of Y?
(c) What is the conditional probability distribution of X, given that Y = 1?
(d) What is E (X|Y = 1)?
(e) What is Cov (X, Y )?
(f) Are X and Y independent random variables?