Question: An investment firm offers its customers municipal
An investment firm offers its customers municipal bonds that mature after varying numbers of years. Given that the cumulative distribution function of T, the number of years to maturity for a randomly selected bond, is
find
(a) P(T = 5);
(b) P(T > 3);
(c) P(1.4 (d) P(T ≤ 5 | T ≥ 2).
Transcribed Image Text:
(0, t<1, 1
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> A candy company distributes boxes of chocolates with a mixture of creams, toffees, and cordials. Suppose that the weight of each box is 1 kilogram, but the individual weights of the creams, toffees, and cordials vary from box to box. For a randomly selec
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> Determine the values of c so that the following functions represent joint probability distributions of the random variables X and Y: (a) f(x, y) = cxy, for x = 1, 2, 3; y = 1, 2, 3; (b) f(x, y) = c|x − y|, for x = −2, 0, 2; y = −2, 3.
> If the probability that a fluorescent light has a useful life of at least 800 hours is 0.9, find the probabilities that among 20 such lights (a) exactly 18 will have a useful life of at least 800 hours; (b) at least 15 will have a useful life of at least
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> An important factor in solid missile fuel is the particle size distribution. Significant problems occur if the particle sizes are too large. From production data in the past, it has been determined that the particle size (in micrometers) distribution is
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> The time to failure in hours of an important piece of electronic equipment used in a manufactured DVD player has the density function (a) Find F(x). (b) Determine the probability that the component (and thus the DVD player) lasts more than 1000 hours b
> From a box containing 4 black balls and 2 green balls, 3 balls are drawn in succession, each ball being replaced in the box before the next draw is made. Find the probability distribution for the number of green balls.
> From a box containing 4 dimes and 2 nickels, 3 coins are selected at random without replacement. Find the probability distribution for the total T of the 3 coins. Express the probability distribution graphically as a probability histogram.
> Find the probability distribution for the number of jazz CDs when 4 CDs are selected at random from a collection consisting of 5 jazz CDs, 2 classical CDs, and 3 rock CDs. Express your results by means of a formula.
> Find the cumulative distribution function of the random variable W in Exercise 3.8. Using F(w), find (a) P(W >0); (b) P(−1 ≤W
> Three cards are drawn in succession from a deck without replacement. Find the probability distribution for the number of spades.
> Consider the density function (a) Evaluate k. (b) Find F(x) and use it to evaluate P(0.3
> For the density function of Exercise 3.18, find F(x), and use it to evaluate P(3 ≤X
> An overseas shipment of 5 foreign automobiles contains 2 that have slight paint blemishes. If an agency receives 3 of these automobiles at random, list the elements of the sample space S, using the letters B and N for blemished and non-blemished, respect
> For the density function of Exercise 3.17, find F(x). Use it to evaluate P(2 < X < 2.5). Exercise 3.17: A continuous random variable X that can assume values between x = 1 and x = 3 has a density function given by f(x) = 1/2.
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> A continuous random variable X that can assume values between x = 2 and x = 5 has a density function given by f(x) = 2(1 + x)/27. Find (a) P(X
> A continuous random variable X that can assume values between x = 1 and x = 3 has a density function given by f(x) = 1/2. (a) Show that the area under the curve is equal to 1. (b) Find P(2 < X < 2.5). (c) Find P(X ≤ 1.6).
> Construct a graph of the cumulative distribution function of Exercise 3.15.
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> Classify the following random variables as discrete or continuous: X: the number of automobile accidents per year in Virginia. Y : the length of time to play 18 holes of golf. M: the amount of milk produced yearly by a particular cow. N: the number of eg
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> The probability that an automobile being filled with gasoline also needs an oil change is 0.25; the probability that it needs a new oil filter is 0.40; and the probability that both the oil and the filter need changing is 0.14. (a) If the oil has to be c
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> In USA Today (Sept. 5, 1996), the results of a survey involving the use of sleepwear while traveling were listed as follows: (a) What is the probability that a traveler is a female who sleeps in the nude? (b) What is the probability that a traveler is
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> The probabilities are 0.4, 0.2, 0.3, and 0.1, respectively, that a delegate to a certain convention arrived by air, bus, automobile, or train. What is the probability that among 9 delegates randomly selected at this convention, 3 arrived by air, 3 arrive
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> As the situation of Exercise 2.69 might suggest, statistical procedures are often used for control of quality (i.e., industrial quality control). At times, the weight of a product is an important variable to control. Specifications are given for the weig
> Consider the situation of Exercise 2.69. Suppose 50,000 boxes of detergent are produced per week and suppose also that those underfilled are “sent back,” with customers requesting reimbursement of the purchase price. Suppose also that the cost of product
> Four students are selected at random from a chemistry class and classified as male or female. List the elements of the sample space S1, using the letter M for male and F for female. Define a second sample space S2 where the elements represent the number
> It is common in many industrial areas to use a filling machine to fill boxes full of product. This occurs in the food industry as well as other areas in which the product is used in the home, for example, detergent. These machines are not perfect, and in
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> Consider the situation of Example 2.32 on page 58. (a) What is the probability that no more than 4 cars will be serviced by the mechanic? (b) What is the probability that he will service fewer than 8 cars? (c) What is the probability that he will service
> Factory workers are constantly encouraged to practice zero tolerance when it comes to accidents in factories. Accidents can occur because the working environment or conditions themselves are unsafe. On the other hand, accidents can occur due to carelessn
> According to a genetics theory, a certain cross of guinea pigs will result in red, black, and white offspring in the ratio 8:4:4. Find the probability that among 8 offspring, 5 will be red, 2 black, and 1 white.
> Consider the situation of Exercise 2.64. Let A be the event that the component fails a particular test and B be the event that the component displays strain but does not actually fail. Event A occurs with probability 0.20, and event B occurs with probabi
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> In a poker hand consisting of 5 cards, find the probability of holding (a) 3 aces; (b) 4 hearts and 1 club.
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> If each coded item in a catalog begins with 3 distinct letters followed by 4 distinct nonzero digits, find the probability of randomly selecting one of these coded items with the first letter a vowel and the last digit even.
> From past experience, a stockbroker believes that under present economic conditions a customer will invest in tax-free bonds with a probability of 0.6, will invest in mutual funds with a probability of 0.3, and will invest in both tax-free bonds and mutu
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