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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 9PPS

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3.
The frequency distribution of a measurable characteristic
varying between 0 and 2 is represented by the following :
f (x) = x³,
= (2 – x)³,
0<x<1;
1<xS2.
%3|
Calculate the standard deviation and also the mean deviation about
mean.

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Please help me answer (d) and (e).
"Time headway" in traffic flow is the elapsed time between the time that one car finishes passing a fixed point and the instant that the next car begins to pass that point. Let X = the time headway for two randomly chosen consecutive cars on a freeway during a period o heavy flow (sec). Suppose that in a particular traffic environment, the distribution of time headway has the following form. x! f(x) = (a) Determine the value of k for which f(x) is a legitimate pdf. (b) Obtain the cumulative distribution function. F(x) = x< 1 (c) Use the cdf from (b) to determine the probability that headway exceeds 2 sec. (Round your answer to three decimal places.) 016 Use the cdf from (b) to determine the probability that headway is between 2 and sec. (Round your answer to three decimal places.) .014 (d) Obtain the mean value of headway and the standard deviation of headway. (Round your answers to three decimal places.) mean .6 standard deviation (e) What is the probability that headway is within 1…
"Time headway" in traffic flow is the elapsed time between the time that one car finishes passing a fixed point and the instant that the next car begins to pass that point. Let X = the time headway for two randomly chosen consecutive cars on a freeway during a period of heavy flow (sec). Suppose that in a particular traffic environment, the distribution of time headway has the following form. x> 1 f(x) = (a) Determine the value of k for which f(x) is a legitimate pdf. (b) Obtain the cumulative distribution function. x> 1 F(x) = xs1 (c) Use the cdf from (b) to determine the probability that headway exceeds 2 sec. (Round your answer to four decimal places.) Use the cdf from (b) to determine the probability that headway is between 2 and 3 sec. (Round your answer to four decimal places.) (d) Obtain the mean value of headway and the standard deviation of headway. (Round your standard deviation to three decimal places.) mean standard deviation (e) What is the probability that headway is…
6.40) my professor says I have to explain the steps in the solved problems in the picture. Not just copy eveything down from the text.
"Time headway" in traffic flow is the elapsed time between the time that one car finishes passing a fixed point and the instant that the next car begins to pass that point. Let X = the time headway for two randomly chosen consecutive cars on a freeway during a period of heavy flow (sec). Suppose that in a particular traffic environment, the distribution of time headway has the following form. x >1 f(x) =10 xs1 (a) Determine the value of k for which f(x) is a legitimate pdf. (b) Obtain the cumulative distribution function. x> 1 F(x) = xs1 (c) Use the cdf from (b) to determine the probability that headway exceeds 2 sec. (Round your answer to four decimal places.) Use the cdf from (b) to determine the probability that headway is between 2 and 3 sec. (Round your answer to four decimal places.)
"Time headway" in traffic flow is the elapsed time between the time that one car finishes passing a fixed point and the instant that the next car begins to pass that point. Let X = the time headway for two randomly chosen consecutive cars on a freeway during a period of heavy flow (sec). Suppose that in a particular traffic environment, the distribution of time headway has the following form. k x > 1 f(x): .10 X 1 F(x) X < 1 (c) Use the cdf from (b) to determine the probability that headway exceeds 2 sec. (Round your answer to four decimal places.) Use the cdf from (b) to determine the probability that headway is between 2 and 3 sec. (Round your answer to four decimal places.) (d) Obtain the mean value of headway and the standard deviation of headway. (Round your standard deviation to three decimal places.) mean standard deviation (e) What is the probability that headway is within 1 standard deviation of the mean value? (Round your answer to three decimal places.)
1 3. f (x) 4 6. Let f be a function with selected values given in the table above. Which of the following statements must be true? I. By the Intermediate Value Theorem, there is a value c in the interval (0, 3) such that f (c) = 2. II. By the Mean Value Theorem, there is a value c in the interval (0, 3) such that f' (c) = 2. II. By the Extreme Value Theorem, there is a value c in the interval (0, 3 such that f (c) < f (x) for all a in the interval (0, 3. A None I only Il only 1, II, and III
A3. (i) Show that the derivative of the following distribution T = H (x) — 2H (2 - x) where H(x) is the Heaviside step function, is do +282. (ii) Given the following function f(t) = t> 0 t < 0 -et show that its distribution derivative is given by 26 +h, where he¯|t|. =
5. Let V denote the volume of water held in a 1-liter bottle. The pdf of V is f(v) = 90v³ (1v) 0 < v<1 (a) Graph the pdf. Then obtain the cdf of V and graph it. (b) What is P(V <.5) [i.e., F(.5)]? (c) Using part (a), what is P(.25 < V<.5)? What is P.(.25
Prove that d-function is the distribution derivative of the Heaviside function { if x > 0, if x < 0. H(x) =
6. Given the pdf f(x)=B(1+x)(1+P) x>0 Find the MLE of ß
If f(x)=sin(x/2) then there exists a number c in the interval Tt/2

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