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Product quality and advertising An inferior product with a large advertising budget does well when it is introduced, but sales decline as people discontinue use of the product. Suppose that the rate of weekly sales revenue is given by
(a) Find the function that describes the weekly sales.
(b) Find the sales for the first week and the ninth week.
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Chapter 12 Solutions
MATHMATICAL APPLICATIONS FOR THE MANAGEM
- 6.82 6.83 6.84 6.85 *6.86 6.87 If Y is a continuous random variable and m is the median of the distribution, then m is such that P(Ym) = P(Y ≥ m) = 1/2. If Y₁, Y2,..., Y, are independent, exponentially dis- tributed random variables with mean ẞ and median m, Example 6.17 implies that Y(n) = max(Y₁, Y., Y) does not have an exponential distribution. Use the general form of FY() (y) to show that P(Y(n) > m) = 1 - (.5)". Refer to Exercise 6.82. If Y₁, Y2,..., Y,, is a random sample from any continuous distribution with mean m, what is P(Y(n) > m)? Refer to Exercise 6.26. The Weibull density function is given by -my" m-le-y/a f(y)= α 0. y > 0, elsewhere, where a and m are positive constants. If a random sample of size n is taken from a Weibull distributed population, find the distribution function and density function for Y(1) = min(Y1, Y2,Y). Does Y(1) = have a Weibull distribution? Let Y₁ and Y2 be independent and uniformly distributed over the interval (0, 1). Find P(2Y(1) 0, elsewhere,…arrow_forwardWhich of the functions shown below is differentiable at = 0? Select the correct answer below: -7-6-5-4- -6-5-4-3-21, -7-6-5-4-3-2 -7-6-5-4-3-2-1 2 4 5 6 -1arrow_forwardRafael needs to make a total of 50 deliveries this week. So far he has completed 28 of them. What percentage of his total deliveries has Rafael completed?arrow_forward
- Please ensure that all parts of the question are answered thoroughly and clearly. Include a diagram to help explain answers. Make sure the explanation is easy to follow. Would appreciate work done written on paper. Thank you.arrow_forwardA study investigating a new test for diagnosing acute myocardial infarction (AMI) has just been initiated. The sensitivity of the test is estimated at 75% and the specificity at 80%. The study enrolls 600 patients, of whom 200 are confirmed AMI cases as determined by the diagnostic gold standard. How many false negatives are to be expected in the study? A. 50 B. 80 C. 120 D. 150 E. 400arrow_forwardchoose the correct graph belowarrow_forward
- 6.26 The Weibull density function is given by e-y/a f(y) = α 0. y > 0, elsewhere, where a and m are positive constants. This density function is often used as a model for the lengths of life of physical systems. Suppose Y has the Weibull density just given. Find a the density function of UY". b E(Y) for any positive integer k. 6.27 Let Y have an exponential distribution with mean ẞ. 6.28 6.29 a Prove that W = √Y has a Weibull density with α = ẞ and m = 2. b Use the result in Exercise 6.26(b) to give E(Yk/2) for any positive integer k. Let Y have a uniform (0, 1) distribution. Show that U = -2ln(Y) has an exponential distri- bution with mean 2. The speed of a molecule in a uniform gas at equilibrium is a random variable V whose density function is given by 6.30 6.31 6.32 f(v) = av²e-by², v > 0, where b = m/2kT and k, T, and m denote Boltzmann's constant, the absolute temperature, and the mass of the molecule, respectively. a Derive the distribution of W = mV2/2, the kinetic energy of…arrow_forwardcorrect answer is Acould you please show me how to compute using the residue theoremarrow_forwardthe correct answer is A please explainarrow_forward
- 1 2 3 4 5 6 7 8 9 10 Question 9 Suppose a charity received a donation of $21.9 million. If this represents 56% of the charity's donated funds, what is the total amount of its donated funds? Please round the answer to the nearest million dollars.arrow_forwardcorrect answer is B could you please explainarrow_forwardPlease ensure that all parts of the question are answered thoroughly and clearly. Include a diagram to help explain answers. Make sure the explanation is easy to follow. Would appreciate work done written on paper. Thank you.arrow_forward
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
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