Suppose each round of a game consists of rolling a 6-side die, flipping a coin, and drawing a card from a 52 card deck. You win a round if you roll an even, flip a heads, and draw a face card. It costs you 1 dollar if you lose a round. Let X be the number of rounds you lose before you finally win one. What is the pmf of X? If you get $60 for winning a round, should you play this game to try to make money? 7.Grasshoppers are distributed at random in a large field according to a Poisson process with parameter l=2 per square yard. How large should the radius R of a circular sampling region be taken so that the probability of finding at least one in the region equals .99? 8.Of the people passing through an airport metal detector, .5% activate it; let X =the number among a randomly selected group of 500 who activate the detector. What is the (approximate) pmf of X9.Let p1 denote the probability that any particular code symbol is erroneously transmitted through a communication system. Assume that on different symbols, errors occur independently of one another. Suppose also that with probability p2 an erroneous symbol is corrected upon receipt. Let X denote the number of correct symbols in a message block consisting of n symbols (after the correction process has ended). What is the probability distribution of 10.A plan for an executive travelers’ club has been developed by an airline on the premise that 10% of its current customers would qualify for membership. Assuming the validity of this premise, among 25 randomly selected current customers what is the distribution of the number of customers who qualify for membership? 11.Each of 12 refrigerators of a certain type has been returned to a distributor because of an audible, high-pitched, oscillating noise when the refrigerators are running. Suppose that 7 of these refrigerators have a defective compressor and the other 5 have less serious problems. If the refrigerators are examined in random order, let ? X ?
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- Fall '08
- Binomial, Probability distribution, Randomness