A company pays a fine if the time to process requests exceeds 7 seconds. Processing a request consists of two tasks: (a) retrieving the file, which takes an amount of time X that is exponentially distributed with mean 5 seconds, and (b) processing the file, which takes an amount of time Y that is independent of X and uniformly distributed between 1 second and 3 seconds. Given that the mean time to process a request is 7 seconds, the company views the fine as unfair, because it will have to pay the fine on half of its requests. In this problem you will investigate whether the company is correct by computing the actual fraction of requests for which the fine will have to be paid 1) Find the joint PDF fx,y (x, y) of X and Y. 2) Sketch the region for which fxy(x, y) is positive, and the subregion over which the company will have to pay the fine. 3) Carry out the integration and compute P(X+Y> 7), and draw a conclusion on whether the company was right or wrong.

A company pays a fine if the time to process requests exceeds 7 seconds. Processing a request consists of two tasks: (a) retrieving the file, which takes an amount of time X that is exponentially distributed with mean 5 seconds, and (b) processing the file, which takes an amount of time Y that is independent of X and uniformly distributed between 1 second and 3 seconds. Given that the mean time to process a request is 7 seconds, the company views the fine as unfair, because it will have to pay the fine on half of its requests. In this problem you will investigate whether the company is correct by computing the actual fraction of requests for which the fine will have to be paid 1) Find the joint PDF fx,y (x, y) of X and Y. 2) Sketch the region for which fxy(x, y) is positive, and the subregion over which the company will have to pay the fine. 3) Carry out the integration and compute P(X+Y> 7), and draw a conclusion on whether the company was right or wrong.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

9⊙10 4 = ?
V-10 oV - 35
2 dr 8.
m² = K 3 H 3 T
Let AABC be a triangle. Fix the points X, Y, and Z on AB, AC, and BC, respectively (as in the figure) such that BX = - = CZ AY = 4. Assume that the area of AXYZ is one and calculate the area of AABC. ХА YC ZB
-5-2 3
Evaluate 3e
d子 2.
A 24 7 C В
Sx? cosh 5xdx