Let X = the headway between two randomly selected consecutive cars (sec). Suppose that in a...
Let X = the headway between two randomly selected consecutive cars (sec). Suppose that in a different traffic environment =, the distribution of time headway has the form:
f(x) = {k/(x^5) if x >= 1, 0 if x <= 1
A: Determine the value of k for which f(x) is a legitimate pdf.
B: Obtain the cumulative distribution function.
C: Use the cdf form (b) to determine the probability that headway exceeds 2 sec and also the probability that headway is between 1 and 3 sec.
D: Obtain the mean value of headway and the standard deviation of headway.
E: What is the probability that headway is within 1 standard deviation of the mean value?
Homework Answers
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Let X = the headway between two randomly selected consecutive
cars (sec). Suppose that in a...
"Time headway" in traffic flow is the elapsed time between the time that one car finishes...
"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) = 6 10 X51 (a)...
9. + 5/7 points Previous Answers DevoreStat9 4.E.013. My Notes + Ask Your Teacher 'Time headway"...
9. + 5/7 points Previous Answers DevoreStat9 4.E.013. My Notes + Ask Your Teacher '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...
need help "Time headway" in traffic flow is the elapsed time between the time that one...
need help
"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 R 0.17 0.17 0.5) x 0.5 3 0 otherwise (a) What is the probability that time headway is at...
Cars arrive at a parking garage at a rate of 90 veh/hr according to the Poisson...
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Time headway in traffic non he elapsed tin e between the t ne hat one car finshes passing a fixed point and the nstant that he next car begins o pass that point. Let χ period af haavy flow. The pdf af X is the folowing. the tinie heed ay r two randomly chosen consecu ve cars on a free ay during a tx) - 0.16e-0.6 (a) what is the probability that time headway i at moat 5 sc? (Raund...
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15. (10 points) A. Draw a graph of the probability distribution function (PDF) for the uniform distribution that is defined to be non-zero and constant between 1 and 10. Label the x and y-axes for the graph. (3 points) B. On the same graph draw the cumulative distribution function (CDF) for the uniform distribution. Clearly identify each line (PDF or CDF) in the graph. (3 points) C. In words, express the mathematical relationship that exists between any CDF and the...
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6. (Sec. 5.4) Let X denote the price for a randomly selected bouquet of 10 tulips....
6. (Sec. 5.4) Let X denote the price for a randomly selected bouquet of 10 tulips. Suppose the mean value of X is $17.50 and the standard deviation of X is $6.00. (a) Is it plausible that X is normally distributed? Explain why or why not. (b) For a random sample of 55 such bouquets, what is the approximate probability that the sample mean bouquet cost is between $15.00 and $25.00? (c) For a random sample of 55 such bouquets,...
Let X denote the amount of space occupied by an article placed in a 1-ft3 packing...
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"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) = 6 10 X51 (a)...
9. + 5/7 points Previous Answers DevoreStat9 4.E.013. My Notes + Ask Your Teacher '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...
need help
"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 R 0.17 0.17 0.5) x 0.5 3 0 otherwise (a) What is the probability that time headway is at...
Cars arrive at a parking garage at a rate of 90 veh/hr according to the Poisson distribution. () In form of a table, write down the probability density and cumulative probabilities for the random variable Xrepresenting "the number of arrivals per minute forx -0 to 6, correct your answer to nearest 4 decimal places. P(X=x) F(x) P(Xsx) Find x such that there is at least 95% chance that the arrival rate is less than x vehicles per minutes. (ii) ii)...
Time headway in traffic non he elapsed tin e between the t ne hat one car finshes passing a fixed point and the nstant that he next car begins o pass that point. Let χ period af haavy flow. The pdf af X is the folowing. the tinie heed ay r two randomly chosen consecu ve cars on a free ay during a tx) - 0.16e-0.6 (a) what is the probability that time headway i at moat 5 sc? (Raund...
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