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In Problems 17–20, find the mean, variance, and standard deviation.
20.
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Chapter 11 Solutions
EBK CALCULUS FOR BUSINESS, ECONOMICS, L
- Problem 2. Show that D₁ = (DFFITS;)² MSE (1) (p+1)MSE' where MSE() is the mean squared error after the i-th data point is omitted.arrow_forwardSuppose the relationship between Y and X is given by: Y = 25 - 3X + error By how much does the expected value of Y change if X decreases by 1 unit?arrow_forwardSituation 9. Suppose that X has a lognormal distribution with parameters 0 = -2 and ² = 9. Determine the following: 18. P(500 x) = 0.1 20. The variance of X.arrow_forward
- 4 Let f(x) = (1/10)(x-3)^2 for x = 1, 2, 3, 4, 5 %3D Find the standard deviation of X. For the instructor, this was question 11. / 1.8 X 3.1 X 3.4 X 3.5 X 9.4 X 12.4arrow_forwardIf X N(49, 16), then the standard deviation of X equalsarrow_forwardSuppose the relationship between Y and X is given by: Y = 25 - 3X + error By how much does the expected value of Y change if X decreases by 2 units?arrow_forward
- 19. In Saint Tropez, the probability that it rains on a given day is 10%. Given that it rains, the amount of rain has a density of f(x) = (1/3)e-/3. Find the variance of the amount of rain on a given day. A. 0.9 B. 1.7 C. 3.0 E. 9.0 D. 4.4arrow_forwardProblem 1. A civil engineer is studying a left-turn lane that is long enough to hold seven cars. Let X be the number of cars in the lane at the end of a randomly chosen red light. The engineer believes that the probability that X = x is proportional to (x+1)(8 - x) for x = 0, 1, - --, 7. (A) Find the PMF of X. (B) Find the probability that X is at least five.arrow_forwardSuppose that f (x) = (3/2)x2 for −1< x < 1. Determine the mean and standard deviation of X.arrow_forward
- The mean time to expose a single panel in a circuit-board plant is 2 minutes with a standard deviation of 1.5 minutes. What is the natural coefficient of variation? If the times remain independent, what will be the mean and variance of a job of 60 panels? What will be the coefficient of variation of the job of 60? (Hint: The Central Limit Theorem for the Sum can be applied to this question.) Now suppose times to failure on the expose machine are exponentially distributed with a mean of 60 hours and the repair time is also exponentially distributed with a mean of 2 hours. What are the effective mean and CV of the process time for a job of 60 panels? (Hint: The mean and the standard deviation of an exponential distribution are the same.)arrow_forwardThe mean time to expose a single panel in a circuit-board plant is 2 minutes with a standard deviation of 1.5 minutes. What is the natural coefficient of variation? If the times remain independent, what will be the mean and variance of a job of 60 panels? What will be the coefficient of variation of the job of 60?(Hint: The Central Limit Theorem for the Sum can be applied to this question.) Now suppose times to failure on the expose machine are exponentially distributed with a mean of 60 hours and the repair time is also exponentially distributed with a mean of 2 hours. What are the effective mean and CV of the process time for a job of 60 panels?(Hint: The mean and the standard deviation of an exponential distribution are the same.) Reconsider the expose machine of Problem 3 with mean time to expose a single panel of 2 minutes with a standard deviation of 1.5 minutes and jobs of 60 panels. As before, failures occur after about 60 hours of run time, but now happen only between jobs…arrow_forwardFor any variable X, if: the standard deviation = and the variance = Var(X) Which of the following statement is true: Select one: a. SD < Var(X) O b. (SD)² = Var(X) (SD) C. SD = [var(x)]²arrow_forward
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