Section4Notes - OR360 Section 4 Notes Conditional...

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OR360 Section 4 Notes Conditional Probability 1 General Write the weekday of your section on your homework! If there is any ambiguity about which section you are in, your homework will not be returned to you in section, but you will have to come and pick it up in Yankun’s or Emmanuel’s office hours. If you have not registered on the Blackboard website, do so now! Your grades will not be recorded until you have registered, and your homework will not be returned to you. 2 Recall: Joint distributions Discrete random variables X,Y may have a joint distribution P { X = x,Y = y } = p ( x,y ). The marginal distribution of a discrete random variable is P { X = x } = y p ( x,y ), similar for P { Y = y } Continuous random variables X,Y may have joint density f X,Y ( x,y ) Analogously, the marginal distribution is f X ( x ) = R y f X,Y ( x,y ) dy , similar for f Y ( y ). Random variables are independent if P { X = x,Y = y } = P { X = x } P { Y = y } (discrete case), or f X,Y ( x,y ) = f X ( x ) f Y ( y ) (continuous case). Example : If the marginal distributions p X ( x ) and p Y ( y ) are known, does this determine the joint distribution? No.
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Section4Notes - OR360 Section 4 Notes Conditional...

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