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Chapter 7: Q.7.42 (page 362)
It follows from Proposition and the fact that the best linear predictor of with respect to is that if then (Why?) Verify this directly
Minimize the expected squared error.
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How many times would you expect to roll a fair die before all sides appeared at least once?
If are independent and identically distributed random variables having uniform distributions over , find
(a) ;
(b) .
Cards from an ordinary deck are turned face up one at a time. Compute the expected number of cards that need to be turned face up in order to obtain
(a) 2 aces;
(b) 5 spades;
(c) all 13 hearts.
The county hospital is located at the center of a square whose sides are miles wide. If an accident occurs within this square, then the hospital sends out an ambulance. The road network is rectangular, so the travel distance from the hospital, whose coordinates are , to the point is . If an accident occurs at a point that is uniformly distributed in the square, find the expected travel distance of the ambulance.
Consider 3 trials, each having the same probability of success. Let denote the total number of successes in these trials. If , what is
(a) the largest possible value of ?
(b) the smallest possible value of }?
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