P Set 1 - 1 MGTECON 603, Econometrics I Fall 2009 PROBLEM...

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1 MGTECON 603, Econometrics I Jules H. van Binsbergen Fall 2009 Stanford GSB PROBLEM SET 1 Due: Friday October 2 nd in class 1. Six fair dice are rolled one time. What is the probability that each face (each number one through six) appears? 2. If two fair dice are tossed, what is the smallest number of throws for which the prob- ability of getting at least one double six exceeds 0.5. (Pascal and M´ er´ e corresponded about this problem in 1654). 3. Two dice are thrown and three events are de±ned as follows: A means ”odd face with ±rst die”; B means ”odd face with second die”; and C means ”odd sum” (one face is odd, one face is even). If each of the 36 sample points has probability 1/36, then (a) Show that the events are pairwise independent. (b) Show that the events are not jointly independent. 4. Through mid-1999, the Boeing Co. had manufactured 746 aircraft in its 767-model series. Exactly two of these 746 aircraft had crashed. The ±rst occured in 1989, and was the 283rd aircraft manufactured in the 767-series. The second crash occurred in
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P Set 1 - 1 MGTECON 603, Econometrics I Fall 2009 PROBLEM...

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