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Chapter 7: Q 7.6 (page 352)
A fair die is rolled times. Calculate the expected sum of the rolls.
The expected sum of the rolls value are.
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If 10 married couples are randomly seated at a round table, compute
(a) The expected number and
(b) The variance of the number of wives who are seated next to their husbands.
An urn contains balls, of whichare red and 8 are blue. From this urn, 12 balls are randomly withdrawn. Let X denote the number of red and Y the number of blue balls that are withdrawn. Find Cov(X, Y)
(a) by defining appropriate indicator (that is, Bernoulli) random variables
such that
(b) by conditioning (on either X or Y) to determine
Ten hunters are waiting for ducks to fly by. When a flock of ducks flies overhead, the hunters fire at the same time, but each chooses his target at random, independently of the others. If each hunter independently hits his target with probability ., compute the expected number of ducks that are hit. Assume that the number of ducks in a flock is a Poisson random variable with mean .
The joint density function ofandis given by
Find and show that
Cards from an ordinary deck of playing cards are turned face upon at a time. If the 1st card is an ace, or the nd a deuce, or the rd a three, or ...,or the th a king,or the an ace, and so on, we say that a match occurs. Note that we do not require that the (n + ) card be any particular ace for a match to occur but only that it be an ace. Compute the expected number of matches that occur.
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