Two contractors (1 and 2) placed a bid on a road construction project. They were each asked to provide percentile estimates of the time (x, in years) it would take the road to undergo a major maintenance after its completion. We seek to maximize this time variable x, as larger values imply better structural integrity as well as cheaper rejection of the net present value for maintenance cost.The CDC for contractor 1, The CDC for contractor 2, IF(x) is as follows: 10 IF(X) (a) Graph the CDC for each contractor.
(b) Calculate analytically the expected value of x for each contractor. [Hint: See Slide (c) Based alone on your computed expected values from (b), which contractor would you recommend? (d) What analysis can you supplement with (c) to improve your recommendation? Page 1 of 2 Problem 2: (1 apt) The number of cyber attacks (X) to E-Lake, an online auction site, is Poisson with mean arrival rate of 30 attacks per hour.Show detailed calculations to answer the following: (a) What is the probability that there is no attack in the next minute? (b) Calculate the minimum value of x (per minute) that satisfies Pr X < x > 0. 98. (c) Suppose the time between each attack is exponentially distributed with the same mean arrival rate given previously.
Starting at t=O (when the auction site opens its cuisines in a given day), what is the probability of an attack within the first 30 seconds? D) Calculate the median time, in seconds. Problem 3: (2 puts) A network administrator is considering two mutually exclusive alternatives for an intrusion detection system, A and B. The reliability distributions of the systems are triangular, with parameters
