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

This preview shows page 1. Sign up to view the full content.

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?
This is the end of the preview. Sign up to access the rest of the document.

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 ﬁve 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 ﬂush in a hand of poker? A Royal straight ﬂush: ten, jack, queen, king and ace of the same suit? 1...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online