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Probability and Statistics Quiz One Solution Statement A: False : Let . Events and are independent and events and are in dependent. Obviously, events and are not independent. Sol A C A B B C A C Statement B: False : Let be an event with [ ] 1. Events and are indepedent. [ ] [ ] [ ] [ ] 1 [ ] is a subset of . Sol B P B A B P A B P A P B P A P A A B   Statement C: False : Let [ ] 0 and [ ] 0. If Events and are mutually exclusive, then [ ] 0 [ ] [ ]. Events and are not independent. Sol P A P B A B P A B P A P B A B Statement D: True : Let { }, { }, : universal set. [ ] 0, [ ] [ ] 1 [ ] [ ] [ ( )] [( ) ( )] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ | ] [ ] [ | ] [ ] [ | ] [ ] [ | ] [ ] Sol B X x C X x S P B C P B C P S P A P A S P A B C P A B A C P A B P A C P A B P A C P B P C P B P C P A B P B P A C P C P A X x P X x P A X x P X x

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Unformatted text preview:                         [ | ] ( ) [ | ](1 ( )) X X P A X x F x P A X x F x     Statement E: True 1 : The pdf of is represented by ( ). ( ) is an even function. ( ) ( ) ( ) 1 ( ) 1 ( ) ( ) ( ) 1 1 ( ) ( ) ( ) increases monotonically with its a X X x x X X X X X x X u X u X u X u X Sol X f x f x F x f t dt f t dt f t dt F x F x u F x u F x F x F x                            1 rgument u u x x x    ...
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