the arrival time of a professor to his office is a continuousr.v uniformly distr
ID: 1830446 • Letter: T
Question
the arrival time of a professor to his office is a continuousr.v uniformly distributed over the hour between 8a.m and 9 a.mdefine the events: A= {the professor has not arrived by 8.30 A.M} B={the professor will arrive by 8.31 A.M} find A.p[B/A]. B.p[A/B]. the arrival time of a professor to his office is a continuousr.v uniformly distributed over the hour between 8a.m and 9 a.mdefine the events: A= {the professor has not arrived by 8.30 A.M} B={the professor will arrive by 8.31 A.M} find A.p[B/A]. B.p[A/B].Explanation / Answer
Not quite sure what your notation means is A/B - A given B (i.e. A| B) or A not B (set exclusion, A B). I'll do bothpossibilities: a. p[BA] = p[the professor arrives by 8.31 and the professordoesn't not arrive by 8.30] = p[the professor arrives by 8.30] =1/2 p[x|A] is a random variable uniformly distributed over the hourbetween 8.30am and 9am, so p[B|A] = 1/30. b. p[AB] = p[the professor does not arrive by 8.30 and theprofessor does not arrive by 8.31] = p[the professor arrivesbetween 8.31 and 9] = 29/60. p[x|B] is a random variable uniformly distributed over the hourbetween 8am and 8.31am, so p[A|B] = p[the professor arrives after 8:30 | the professor arrivesbefore 8.31] = 1/31.
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