Pearson eText for Probability and Statistical Inference -- Instant Access (Pearson+)
10th Edition
ISBN: 9780137538461
Author: Robert Hogg, Elliot Tanis
Publisher: PEARSON+
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Question
Chapter 3.2, Problem 15E
a.
To determine
To find: The point at which the maximum value is attained by the
b.
To determine
To find: The point of inflection if
c.
To determine
To construct: The pdf of X when
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Students have asked these similar questions
"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. The pdf of X is the following.
0.17e-0.17(x - 0.5)
- {0.17e-0.1
x ≥ 0.5
otherwise
(a) What is the probability that time headway is at most 6 sec? (Round your answer to three decimal places.)
f(x) =
(b) What is the probability that time headway is more than 6 sec? At least 6 sec? (Round your answers to three decimal places.)
more than 6 sec
at least 6 sec
(c) What is the probability that time headway is between 5 and 6 sec? (Round your answer to three decimal places.)
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 be the time headway for two randomly chosen
consecutive cars (in seconds). Suppose X has pdf
f(x)
=
{*
F(x)
(a) Find the value of k.
(b) Obtain the mean value of headway and the standard deviation of headway.
(c) The cdf of X is
=
x > 1
x ≤ 1
0
1-
x ≤ 1
x>1
Using the cdf, determine the following probabilities.
(i) What is the probability that observed depth is at most 3?
(ii) What is the probability that observed depth is between 3 and 2?
Chapter 3 Solutions
Pearson eText for Probability and Statistical Inference -- Instant Access (Pearson+)
Ch. 3.1 - Show that the mean, variance, and mgf of the...Ch. 3.1 - Let X be a continuous random variable with pdf...Ch. 3.1 - Customers arrive randomly at a bank tellers...Ch. 3.1 - If the mgf of X is M(t)=e5te4tt,t0andM(0)=1,, find...Ch. 3.1 - Let Y have a uniform distribution U(0,1), and let...Ch. 3.1 - A grocery store can order n watermelons from a...Ch. 3.1 - For each of the following functions, (i) find the...Ch. 3.1 - For each of the following functions, (i) find the...Ch. 3.1 - Prob. 9ECh. 3.1 - The pdf of X is f(x)=cx2,1x. (a) Calculate the...
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Similar questions
- Suppose X has PDF fX (x) = 4x(1 − x^2) for 0 < x < 1 (0 everywhere else). Find all mediansand modes for X.(a) Find all medians of X.(b) Find all modes of X.arrow_forward"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…arrow_forward(b) Let X represent the lifetime in months of a certain brand of light bulb. The pdf of X is given by f(x)=K(6-x), 0arrow_forward6. (Sec. 5.1) Two headlights of a car have the following joint pdf for their useful lifetimes X (the left headlight) and Y (the right headlight) ze(y+1) for r> 0.y > 0 f(x, y) 0 otherwise (a) What is the probability that the lifetime X of the left headlight exceeds 2.8? (b) Find the marginal pdfs of X and Y. Are the two lifetimes independent? Justify your answer (c) What is the probability that the lifetime of at least one headlight does not exceed 2.8?arrow_forward(d) At any time, find the mean age of insects in the population. (e) Sketch g(x), the p.d.f. of the age distribution of insects in the population. (f) No calculations are required for this part of the question.Now suppose that a population with the life table function Q(x) thatyou obtained in part (b) is stable but not stationary. Describe brieflyhow the age distribution of the population would differ from that of astationary population with the same life table function if the populationis (i) growing, (ii) declining. Draw rough sketches to show what thep.d.f. of the age distribution might look like in each case.arrow_forward13. a) Determine the average rate of change over the interval x = [1, 5] of the function y = 3x + 1. b) Regardless of the interval, what will the average rate or instantaneous rate of change be for the function y = 3x + 1? Explain. Expand your answer to include linear functions in general.arrow_forwardIn commuting to work, a professor must first get on a bus near her house and then transfer to a second bus. If the waiting time (in minutes) at each stop has a uniform distribution with A = 0 and B = 10, then it can be shown that the total waiting time Y has the pdf f (y) = = 100 Y 5 10 0 ≤ y ≤ 10 10 ≤ y ≤ 20 a. Sketch a graph of the pdf of Y (do on your own paper, you will not be turning this in. It is for your reference only.) [ f(y)dy=[ -∞ b. Verify that [ f (y) dy = 1 10 120 10 = 1 2 + c. What is the probability that the total waiting time is at most 8 minutes? d. What is the probability that the total waiting time is at most 13 minutes? = 1 e. What is the probability that the total waiting time is between 8 and 13 minutes? f. What is the probability that the total waiting time is either less than 7 minutes or more than 14 minutes?arrow_forwardI need help with parts “c”, “d, and “e” thanks.arrow_forwardThe coefficient of thermal expansion, of steel, is given at discrete values oftemperature in Table 1.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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