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| − | If E and F are events in S (sample space) the the conditional probability of E and F is P(E|F) = P(E intersect F). | + | [[Category:MA375]] |
| + | [[Category:math]] | ||
| + | [[Category:discrete math]] | ||
| + | [[Category:lecture notes]] | ||
| + | |||
| + | =[[MA375]]: Lecture Notes= | ||
| + | Fall 2008, Prof. Walther | ||
| + | ---- | ||
| + | ==Some Definitions== | ||
| + | |||
| + | If '''E''' and '''F''' are events in '''S''' (sample space) the the conditional probability of '''E''' and '''F''' is '''P(E|F) = P(E intersect F)'''. | ||
| + | |||
| + | Further : | ||
| + | the conditional probability of "E" given "F" is =<math> \frac {P(EnF)}{P(F)}</math> | ||
| + | |||
| + | ''defn:'' if P(E|F) = P(E) , then E and F are independent events otherwise they are dependant events. | ||
| + | |||
| + | note: independence implies that <math> P(E)= P(E|F) = \frac {P(EnF)}{P(F)}</math> | ||
| + | |||
| + | or P(E).P(F)=P(EnF). | ||
| + | note : if P(E|F) = P(E) | ||
| + | then P(F|E) = P(F) | ||
| + | ---- | ||
| + | [[Main_Page_MA375Fall2008walther|Back to MA375, Fall 2008, Prof. Walther]] | ||
Latest revision as of 08:16, 20 May 2013
MA375: Lecture Notes
Fall 2008, Prof. Walther
Some Definitions
If E and F are events in S (sample space) the the conditional probability of E and F is P(E|F) = P(E intersect F).
Further :
the conditional probability of "E" given "F" is =$ \frac {P(EnF)}{P(F)} $
defn: if P(E|F) = P(E) , then E and F are independent events otherwise they are dependant events.
note: independence implies that $ P(E)= P(E|F) = \frac {P(EnF)}{P(F)} $
or P(E).P(F)=P(EnF).
note : if P(E|F) = P(E)
then P(F|E) = P(F)
