4. [Limit Theorems] Suppose there is a random sample of n calendar days and for each day we observethe number of purchase orders recieved by an online market, {x1, x2, , ..., xn}. Assume that the numberof orders follows the Poisson distribution with the daily intensity parameter A.(a) Suggest a consistent estimator Â for the unobserved parameter A.(b) Using the Central Limit Theorem, derive the asymptotic distribution of Â as n → ∞o.(c) Can you suggest a transformation g(Â) for this estimator such that the asymptotic distributiondoes not depend on the latent parameter \?

Here's a breakdown of the key concepts involved in estimating the rate of events in a Poisson…

Answered: 4. [Limit Theorems] Suppose there is a…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

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Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

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(13) Let X b(6,-) find E(5+6x) and distribution function. 3
(3) Let X = b >(8,-) find E(5+6x) and distribution function.
"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.)
7. (Sec. 3.6) Consider sending packets of data through the internet, and we have a counter that determines the number of missing/corrupted packets. Suppose that number X has a Poisson distribution with parameter 23. = (a) What is the probability that the counter determines that the transmission has exactly one miss- ing/corrupted packet of data? (b) What is the probability that the counter determines that the transmission has at least 3 miss ing/corrupted packets of data? (c) If two transmissions of data across the internet ar that at least one of them does not contain a missing/corrupted packet? e independently selected, what is the probability
(26) Let X b(8,- Var-x) and distribution function.
explain the characteristic function poisson varaite?
Suppose there is a test, φ, that yields the distribution of test outcomes for good drugs and bad drugs seen in the Figure. In this case, is it possible to create a rule for accepting and rejecting drugs that yields no Type I or Type II error? If so, be sure to show this threshold rule explicitly on the graph above. If not, explain why this is impossible.
"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. f(x) = (a) Determine the value of k for which f(x) is a legitimate pdf. F(x) = k x12 0 (b) Obtain the cumulative distribution function. 0 x > 1 x ≤ 1 mean x > 1 (c) Use the cdf from (b) to determine the probability that headway exceeds 2 sec. (Round your answer to four decimal places.) x ≤ 1 Use the cdf from (b) to determine the probability that headway is between 2 and 3 sec. (Round your answer to four decimal places.) standard deviation (d) Obtain the mean value of headway and the standard deviation of headway. (Round your standard deviation to three decimal places.) (e) What is the probability…
"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…
Suppose the customers arrive at a Poisson rate of on eper every 12 minutes, and that the service time is exponential at a rate of one service per 8 minutes. What are the average number of customers in the system(L) and the average time a customer spends in the system(W)? Now suppose that the arrival rate increases 20 percent.What is the corresponding change in L and W?
Suppose the number X of tornadoes observed in a particular region during a 1-year period has a Poisson distribution with λ = 5.
1. Let X1, X,.., X, random sample from distribution be a a Geometric 2....., fx (x) = p(1– p)*| F, (y,) = ? x-1 x=1,2,3,.... Fy, (y,) = ? P(Y, <1) =? а. b. С.

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