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A gambler makes a sequence of independent bets. In each bet, he wins $1 with probability p. What is the probability that the gambler will end up with $n?
Given the probability of bad weather on a given day, obtain an expression for the probability that the professor will teach her class on that day.
The cellular system has a total capacity of c bits/sec. What is the probability that more users want to use the system than the system can accommodate?
Suppose that any one plant can produce enough electricity to supply the entire city. What is the probability that the city will experience a black-out?
The system is operational if at least K out of the n components are operational. What is the probability that the system is operational?
How can they use the biased coin to make a decision so that option (opera or the movies is equally likely to be chosen?
What is the probability that the sibling is male? Assume that every birth results in a boy with probability 1/2, independent of other births.
Assuming independent coin tosses, show that the probability that after all coins have been tossed, Bob will have gotten more heads than Alice is 1/2.
The release of two out of three prisoners has been announced. but their identity is kept secret. What is wrong with this line of reasoning?
What is the probability that at the end of the four exchanges all the balls will be in the jar where they started?
Show that the probability that the last ball is white is the same as the probability that the first ball is white, i.e. , it is m/(m + n).
The first player to remove a white ball wins. Develop a recursive formula that allows the convenient computation of probability that the starting player wins.
Find the probability that Boris wins the match for each of the Play bold in both games 1 and 2 and Play timid in both games 1 and 2.
If one of the four is defective, the batch is rejected. What is the probability that the batch is accepted if it contains five defectives?
We are given three coins: one has heads in both faces, the second has tails in both faces. What is the probability that the opposite face is tails?
A coin is tossed twice. Alice claims that the event of two heads is at least as likely if we know. How can we generalize Alice's reasoning?
How many hours will she work if she earns $20 per hour? Find a formula for her labor supply curve. Is it upward or downward sloping? Why?
How would you measure consumer surplus if the demand curve is upward sloping? Warning: this is a trick question.
What is the efficient method of production for Dewey, Cheetham, and Howe? Graph its production possibilities set. What is its production function?
The number of pounds of coffee they pack depends on the number of workers they hire. Graph Pete and Mary's production function.
Emily draws cartoons that she sells to her classmates. What is her marginal product of labor at one, two, three, and four hours of work?
Its marginal product of labor is MPL = 3L2- 400L + 10,000. At what amount of labor input are the firm's average and marginal product of labor equal?
In general, the variance of the distribution of an estimator decreases when the sample size. Is it correct to describe the estimator as becoming more efficient?
A random variable X is defined to be the difference between higher value and the lower value when two dice are thrown. Find the probability distribution for X.
Perform a logarithmic regression of expenditure on your category of consumer expenditure on income and price using an AR(1) estimation technique.