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Chapter 4: Q. 4. 26 (page 172)
Prove
Hint: Use integration by parts.
The idea of the proob is integrating by parts the right side of the equation times.
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Suppose in Problem 4.72 that the two teams are evenly matched and each has probability 1 2 of winning each game. Find the expected number of games played.
From a set of randomly chosen people, let denote the event that persons and have the same birthday. Assume that each person is equally likely to have any of the 365 days of the year as his or her birthday. Find
(a) ;
(b) ;
(c) .
What can you conclude from your answers to parts (a)-(c) about the independence of the events ?
In Problem for if the coin is assumed fair, what are the probabilities associated with the values that X can take on?
Suppose that balls are put into boxes, with each ball independently being put in box with probability
(a) Find the expected number of boxes that do not have any balls.
(b) Find the expected number of boxes that have exactly ball.
In response to an attack of missiles, antiballistic missiles are launched. The missile targets of the antiballistic missiles are independent, and each antiballstic missile is equally likely to go towards any of the target missiles. If each antiballistic missile independently hits its target with probability . use the Poisson paradigm to approximate the probability that all missiles are hit.
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