B2 Answer ALL parts (a) — (c). (a) An engineering company is manufacturing integrated circuits (ICs) at an equal rate using five different techniques: A, B, C, D and E. An engineer reports that the probabilities of a defective ICs from each technique is: A - 1%, B-2%, C- 3%, D-3%, and E-4%. An IC is selected at random. Calculate the probability that the IC is defective. Illustrate your answer with a probability tree. (b) Your third-year project supervisor gives you the following probability density function with continuous random variable X to model: f(x) = 0.02(10-x) 0≤x≤ 10 Equation (B6) Sketch a graph of the probability density function defined in Equation (B6). Explain and show how you would check mathematically if Equation (B6) is a valid probability density function. Explain all the steps used in your proof. (c) A civil engineer finds an abandoned building contains on average 2 broken bricks per 800m². Define a probability distribution, P(x) for the number of broken bricks (x) in an area of 400m². Hence calculate the probability of there been more than 4 broken bricks in a 400m² area. Explain any assumptions made in your calculations and answers.

B2 Answer ALL parts (a) — (c). (a) An engineering company is manufacturing integrated circuits (ICs) at an equal rate using five different techniques: A, B, C, D and E. An engineer reports that the probabilities of a defective ICs from each technique is: A - 1%, B-2%, C- 3%, D-3%, and E-4%. An IC is selected at random. Calculate the probability that the IC is defective. Illustrate your answer with a probability tree. (b) Your third-year project supervisor gives you the following probability density function with continuous random variable X to model: f(x) = 0.02(10-x) 0≤x≤ 10 Equation (B6) Sketch a graph of the probability density function defined in Equation (B6). Explain and show how you would check mathematically if Equation (B6) is a valid probability density function. Explain all the steps used in your proof. (c) A civil engineer finds an abandoned building contains on average 2 broken bricks per 800m². Define a probability distribution, P(x) for the number of broken bricks (x) in an area of 400m². Hence calculate the probability of there been more than 4 broken bricks in a 400m² area. Explain any assumptions made in your calculations and answers.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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