hwk1 - (3) An eight-bit computer word is a sequence of...

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HOMEWORK #1 STATISTICAL INFERENCE (1) As seen in class Boole’s inequality states that P ( n j =1 A i ) n X i =1 P ( A i ) . Use Venn diagrams to convince yourself that Boole’s inequality is true in the case that n = 3. (2) Suppose we conduct an experiment and use relative frequencies to assign probabilities to two two events A and B . (a) If we only know that P ( A ) = . 7 and P ( B ) = . 4, what is the strongest statement we can make about P ( A B ) and P ( A B )? (b) If we only know that P ( A ) = . 6 and P ( B ) = . 2, what is the strongest statement we can make about P ( A B ) and P ( A B )? (c) Under what conditions does Boole’s inequality provide nontrivial in- formation? (d) Under what conditions does Bonferroni’s inequality provide nontrivial information? (e) Is it possible for Boole’s inequality and Bonferroni’s inequality to si- multaneously provide nontrivial information?
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Unformatted text preview: (3) An eight-bit computer word is a sequence of eight 0s and 1s. What is the number of possible eight-bit words? What is the number of eight-bit computer words with exactly three 1s and ve 0s? (4) A standard die is rolled. Determine the probability that the outcomes is a multiple of 3. (5) Two standard distinguishable coins are tossed and the outcome is observed. Determine the probability that both coins land on the same side. (6) Determine the probability that in a group of 30 people, at least 2 have the same birthday. (7) What is the probability of having a Royal straight ush in a hand of poker? A Royal straight ush: ten, jack, queen, king and ace of the same suit? 1...
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