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A coin is tossed twice. Let Z denote the number of heads on the first toss and W the total number of heads on the 2 tosses. If the coin is unbalanced and a head has a 40% chance of occurring, find(a) The joint probability distribution of W and Z;(b) The marginal distribution of W;(c) The marginal distribution of Z;(d) The probability that
1647 
A coin is tossed until the first time a head turns up. If this occurs on the nth toss and n is odd you win 2n/n, but if n is even then you lose 2n/n. Then if your expected winnings exist they are given by the convergent series 1 − 1/2 + 1/3 − 1/4 + • • • called the alternating harmonic series. It is tempting to say that
0168 
A company orders components from Japan for its game player. The prices for the items that it orders are in Japanese yen. When the products are delivered, it must convert dollars into yen to pay the Japanese producer. When its next order is delivered (and must be paid for), it believes that the exchange rate of dollars to yen will take on
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A company services copiers. A review of its records shows that the time taken for a service call can be represented by a normal random variable with a mean of 75 minutes and a standard deviation of 20 minutes. a. What proportion of service calls takes less than 1 hour? b. What proportion of service calls takes more than 90 minutes? c. Ske
01 
A company services home air conditioners. It is known that times for service calls follow a normal distribution with a mean of 60 minutes and a standard deviation of 10 minutes. a. What is the probability that a single service call takes more than 65 minutes? b. What is the probability that a single service call takes between 50 and 70 mi
01 
A consensus forecast is the average of a large number of individual analysts’ forecasts. Suppose the individual forecasts for a particular interest rate are normally distributed with a mean of 5.0 percent and a standard deviation of 1.2 percent. A single analyst is randomly selected. Find the probability that his/ her forecast is: a. A
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A construction company manages two large building projects. Both require about 50 employees with comparable skills. At a meeting, the site managers from the two projects got together to estimate the labor needs of their projects during the coming winter. At the end of the meeting, each manager provided a table that showed how they expecte
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A construction firm bids on a contract. It anticipates a profit of +50,000 if it gets the contract for the full project, and it estimates its profit to be +20,000 on a shared project. The firm estimates there’s a 20% chance it will get the full contract and a 75% chance it will get the shared contract; otherwise, it gets nothing. (a) De
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A construction firm places bids on various portions of the work in building a new office tower. The key bids it submits are for electrical work and for plumbing. The bid for the electrical work estimates 64 weeks of labor (e.g., 1 electrician for 64 weeks or 8 for 8 weeks). The bid for the plumbing estimates 120 weeks of labor. Standard p
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A consultant has three sources of incomefrom teaching short courses, from selling computer software, and from advising on projects. His expected annual incomes from these sources are $20,000, $25,000, and $15,000, and the respective standard deviations are $2,000, $5,000, and $4,000. Assuming independence, find the mean and standard devi
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