EBK APPLIED CALCULUS, ENHANCED ETEXT
6th Edition
ISBN: 9781119399353
Author: DA
Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT
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Chapter 7, Problem 4SYU
To determine
To indicate that the statement “If p(t) is a density function waiting times in minutes at a bank teller, then
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In each of Problems, assume that the variable under consideration has a density curve. Note that the answers required here may be only approximately correct.
The percentage of all possible observations of a variable that lie between 25 and 50 equals the area under its density curve between _______ and _______, expressed as a percentage.
Question 1 : Suppose that the probability density function (p.d.f.) of the life (in weeks) of a certain part is f(x) = 3 x 2 (400)3 , 0 ≤ x < 400. (a) Compute the probability the a certain part will fail in less than 200 weeks. (b) Compute the mean lifetime of a part and the standard deviation of the lifetime of a part. (c) To decrease the probability in part (a), four independent parts are placed in parallel. So all must fail, if the system fails. Let Y = max{X1, X2, X3, X4} denote the lifetime of such a system, where Xi denotes the lifetime of the ith component. Show that fY (y) = 12 y 11 (400)12 , y > 0. Hint : First construct FY (y) = P(Y ≤ y), by noticing that {Y ≤ y} = {X1 ≤ y} ∩ {X2 ≤ y} ∩ {X3 ≤ y} ∩ {X4 ≤ y}. (d) Determine P(Y ≤ 200) and compare it to the answer in part (a)
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Chapter 7 Solutions
EBK APPLIED CALCULUS, ENHANCED ETEXT
Ch. 7.1 - Prob. 1PCh. 7.1 - Prob. 2PCh. 7.1 - Prob. 3PCh. 7.1 - Prob. 4PCh. 7.1 - Prob. 5PCh. 7.1 - Prob. 6PCh. 7.1 - Prob. 7PCh. 7.1 - Prob. 8PCh. 7.1 - Prob. 9PCh. 7.1 - Prob. 10P
Ch. 7.1 - Prob. 11PCh. 7.1 - Prob. 12PCh. 7.1 - Prob. 13PCh. 7.1 - Prob. 14PCh. 7.1 - Prob. 15PCh. 7.1 - Prob. 16PCh. 7.1 - Prob. 17PCh. 7.1 - Prob. 18PCh. 7.2 - Prob. 1PCh. 7.2 - Prob. 2PCh. 7.2 - Prob. 3PCh. 7.2 - Prob. 4PCh. 7.2 - Prob. 5PCh. 7.2 - Prob. 6PCh. 7.2 - Prob. 7PCh. 7.2 - Prob. 8PCh. 7.2 - Prob. 9PCh. 7.2 - Prob. 10PCh. 7.2 - Prob. 11PCh. 7.2 - Prob. 12PCh. 7.2 - Prob. 13PCh. 7.2 - Prob. 14PCh. 7.2 - Prob. 15PCh. 7.2 - Prob. 16PCh. 7.2 - Prob. 17PCh. 7.2 - Prob. 18PCh. 7.2 - Prob. 19PCh. 7.2 - Prob. 20PCh. 7.2 - Prob. 21PCh. 7.3 - Prob. 1PCh. 7.3 - Prob. 2PCh. 7.3 - Prob. 3PCh. 7.3 - Prob. 4PCh. 7.3 - Prob. 5PCh. 7.3 - Prob. 6PCh. 7.3 - Prob. 7PCh. 7.3 - Prob. 8PCh. 7.3 - Prob. 9PCh. 7.3 - Prob. 10PCh. 7.3 - Prob. 11PCh. 7.3 - Prob. 12PCh. 7 - Prob. 1SYUCh. 7 - Prob. 2SYUCh. 7 - Prob. 3SYUCh. 7 - Prob. 4SYUCh. 7 - Prob. 5SYUCh. 7 - Prob. 6SYUCh. 7 - Prob. 7SYUCh. 7 - Prob. 8SYUCh. 7 - Prob. 9SYUCh. 7 - Prob. 10SYUCh. 7 - Prob. 11SYUCh. 7 - Prob. 12SYUCh. 7 - Prob. 13SYUCh. 7 - Prob. 14SYUCh. 7 - Prob. 15SYUCh. 7 - Prob. 16SYUCh. 7 - Prob. 17SYUCh. 7 - Prob. 18SYUCh. 7 - Prob. 19SYUCh. 7 - Prob. 20SYUCh. 7 - Prob. 21SYUCh. 7 - Prob. 22SYUCh. 7 - Prob. 23SYUCh. 7 - Prob. 24SYUCh. 7 - Prob. 25SYUCh. 7 - Prob. 26SYUCh. 7 - Prob. 27SYUCh. 7 - Prob. 28SYUCh. 7 - Prob. 29SYUCh. 7 - Prob. 30SYU
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- With the known values of a = 200,000 and b = 230,000, the first equation for the probability density function for the sales price of a home is found as follows. f(x) = 1/b – a, a ≤ x ≤ b = 1/230,000 − 200000, 200,000 ≤ x ≤ 230,000 = 1/30000, 200,000 ≤ x ≤ 230,000 Everywhere else, the probability density function will just be 0. Therefore, the full probability density function for the sales price of a home follows. f(x) = _______________ 200,000 ≤ x ≤ 230,000 elsewherearrow_forwardFor a certain psychiatric clinic suppose that the random variable X represents the total time (in minutes) that a typical patient spends in this clinic during a typical visit (where this total time is the sum of the waiting time and the treatment time), and that the random variable Y represents the waiting time (in minutes) that a typical patient spends in the waiting room before starting treatment with a psychiatrist. Further, suppose that X and Y can be assumed to follow the bivariate density function fXY(x,y)=λ2e−λx, 0<y<x, where λ > 0 is a known parameter value. (a) Find the marginal density fX(x) for the total amount of time spent at the clinic. (b) Find the conditional density for waiting time, given the total time. (c) Find P (Y > 20 | X = x), the probability a patient waits more than 20 minutes if their total clinic visit is x minutes. (Hint: you will need to consider two cases, if x < 20 and if x ≥ 20.)arrow_forwardIf X is a continuous variable in the range 3 > X > 0 and its distribution function is as follows: F ( x ) = k : ( x3 + x2) find the probability density function?arrow_forward
- Problem 1. A continuous random variable X is defined by f(x)=(3+x)^2/16 -3 ≤ x ≤ -1 =(6-2x^2)/16 -1 ≤ x ≤ 1 =(3-x^2)/16 -1 ≤ x ≤ 3 a)Verify that f(x) is density. b)Find the Meanarrow_forwardIn each of Problems, assume that the variable under consideration has a density curve. Note that the answers required here may be only approximately correct. The area under a density curve that lies to the left of 60 is 0.364. What percentage of all possible observations of the variable are a. less than 60?b. at least 60?arrow_forward
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