EBK APPLIED CALCULUS, ENHANCED ETEXT
6th Edition
ISBN: 9781119399353
Author: DA
Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT
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Chapter 7, Problem 24SYU
To determine
To indicate that the statement “If p (x) is the density function for a quantity x, then the median value T satisfies
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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 Mean
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)
If 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?
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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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Similar questions
- For 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_forwardNeed problem 4 density function is give in problem 2 second imagearrow_forwardIf X is an exponential random variables with rate 1, then its distribution function is given by F(x) = 1 − e−x Show that x = − ln(1 − u).arrow_forward
- 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.arrow_forwardQUESTION 11 The probability density function, f(x), for any continuous random variable X, represents: a. all possible values that X will assume within some interval a ≤ x ≤ b. b. the probability that X takes on a specific value x. c. the height of the density function at x. d. None of these choices.arrow_forward
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