What is the probability that the time of the first event that is observed to occur in a Poisson process with rate λ per unit time, after initiation at t = 0, occurs later than time t = t0, for fixed value t0 ? Justify your answer

T2 #4 Apr 5 Of the international passengers arriving at an airport, 1.5% are selected for luggage inspection. Let X be the number of passengers from a random sample of 400 who are sent for luggage inspection. Use Poisson approximation to X to find the probability that between 6 and 12 passengers inclusive, are sent for luggage inspection.

According to the U.S. Customs and Border Protection Agency, the average airport wait time (time from arrival at the airport until the completion of security screening) at Chicago's O'Hare Inter- national airport is 32 minutes for a passenger arriving during the hours 4-5 PM. Assume the wait time is exponentially distributed so that p(t) = ke-kt for 0≤t<∞, where k is the reciprocal of the average wait time. Assume t is measured in minutes. 1. Sketch a labeled plot of the relevant pdf on the interval [0, 90] minutes (while remembering that it is defined for all t≥ 0.) 2. Set up integrals (you can write p(t) for the integrand) for the following probabilities: (a) Waiting longer than 60 minutes. (b) Waiting shorter than 30 minutes. (c) Waiting between 20 and 40 minutes. 3. Evaluate the probability that the waiting time is longer than 60 minutes (part 2(a) above) and convert to a percentage with two decimal places.

A researcher is interested in finding out how the past average daily values of the stock prices of a firm A determine the current average daily value of its stock price. Let pt ( measured in dollars) denote the average daily value of the stock price of firm A at time t. The researcher collects data on the average daily values of the stock prices of the last quarter of 2017, i.e., t = 1,2, dots,90 and estimates the following autoregressive model with 1 lag of pt: hat(p)t = 2.48 +.05pt.1bar (R)² = 0.512, SER = 13.14. (1.13) (0.64) The standard errors are given in parentheses. Suppose that the actual average daily value of the stock price on January 2, 2018 was $506.12 and the average daily value of the stock price on December 31, 2017 was $445.12. The forecast error in the estimation of the average daily value of the stock price on January 2, 2018 will be $ (Round your answer to two decimal places.) This is all the info in the question

5:47 PM 7 ||| 9 3 М ALEKS Login O PROBABILITY Probabilities involving two mutually exclusive events r Events A and B are mutually exclusive. Suppose event A occurs with probability 0.64 and event B occurs with probability 0.22. Compute the following. (If necessary, consult a list of formulas.) (a) Compute the probability that B occurs or A does not occur (or both). 0 Compute the probability that Explanation Check 0/5 X Start Here G Ⓒ2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center R Dianne V Español ? Accessibi ****

Event A is my wife cooking dinner tonight. It has been determined that P(A) = 0.15. What is P(not A)?