Chapter 8, Problem 42RE

'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?

Suppose a sample Y1, ..., Yn is selected from an exponential distribution with E (Yi) = θ and V (Yi) = θ2. Let θˆ be an estimator of the mean, θ.1. Explain what a parameter is. What is the parameter of interest in this case?2. Name the properties of a good estimator and explain, shortly, what is meant by each. (a)(b) (c)3. Given the properties you discussed in (2) and the parameter of interest identified in (1), what estimator would you propose?4. What would the sampling distribution of this estimator be? Why?

A large sample confidence inerval for the log of the relative risk is: CI = log(p1/p2)+-Z(alpha/2)sqrt[(1-p1/n1p1)+(1-p2/n2p2) Antilogs of the endpoints yield an interval for the true relative risk. Verify the 95% CI of (1.43, 2.30) reported for  the relative risk in the following table (aspin and heart attack study):   myocardial infarction+ Myocardial infarction - total aspirin 189 10845 11034 placebo 104 10933 11037 total 293 21778 22071

A random sample of CO2 levels in a school has a sample mean of x¯=598.4 ppm and sample standard deviation of s=86.7 ppm.  Use the Empirical Rule to determine the approximate percentage of CO2 levels that lie between 338.3 and 858.5 ppm.

True or False? 1/n∑(Xi − X)^2 is an asymptotically unbiased estimator for the variance of X.

Given the following PDF, calculate the following quantities: f(x)=90*(x^8)*(1-x) for 0.7) 9. 0.8507 P(.7

A survey collected data from a random sample of 121 people living in Jade city. The sample average of the distance people travel to reach their workplaces (Y) is 23.28 km and the standard deviation (sy) is 7.48 km. The standard error of the sample average of the distance people travel to reach their workplaces is 68 km. (Round your answer to two decimal places.) Let μy denote the mean of the distance all the people in Jade city travel to reach their workplaces. The p-value of the test Ho: #y #22 km vs. H₁: Hy #22 km is (Round your answer to two decimal places.)

Given pdf f (x) = 1.5x2  for −1< x < 1. Determine variance of X.

When we fit a logistic regression model with a single explanatory term, x, we often assume that logit (pi) Bo + ₁x₂ where, for the ith observation, p; is the probability of a trial being successful and *; is the value of the explanatory variable. Which of the following is a good reason for using the logit link function? We can't use more than one explanatory term unless we use this link function. It allows us to model nonconstant variance in the response variable. It ensures that the probability of success is between 0 and 1. It ensures that the variance of the response is the same for all observations.