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EL630 HW2

# EL630 HW2 - EL630 Homework 2 1(Book:2-8 If A B P A 1 4 and...

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1 EL630: Homework 2 1. (Book:2-8) f , ( ) 1/4, and ( ) 1/3, find ( | ) and ( | ). I A B P A P B P A B P B A = = 2. (Book:2-9) Show that ( | ) ( | ) ( | ) P AB C P A BC P B C = an d( ) ( | ) ( | ) ( ). P ABC P A BC P B C P C = 3. (Book:2-12) A call occurs at time ,where is a random point in the interval (0,10). Find {6 8}. ( ) Find {6 8| 5}. t t P t b P t t > 4. (Book:2-13, ,not required hard ) 1 0 0 1 0 1 0 1 1 The space is the set of all positive numbers. Show that if { | } { } for every and , then { } 1 , where is a constant. ct P t t t t t t P t t t t P t t e c + = =− (Thesolution isinLecture2.) 5. (Book: 2-14) The events A and B are mutually exclusive. Can they be independent? 0 t 0 t 0 + t 1 t 1 t  0 1 2 3 4 5 6 7 8 9 10

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2 6. (Book: 2-23) Box 1 contains 1 white and 999 red balls. Box 2 contains 1 red and 999 white balls. A ball is picked from a randomly selected box. If the ball is red what is the probability that it came from box 1? 7. (Book: 2-24) Box 1 contains 1000 bulbs of which 10% are defective. Box 2 contains 2000 bulbs of which 5% are defective. Two bulbs are picked from a randomly selected box. (a) Find the probability that both bulbs are defective. (b) Assuming that both are

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EL630 HW2 - EL630 Homework 2 1(Book:2-8 If A B P A 1 4 and...

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