**Smog Alert Inspection Analysis**A second-stage smog alert has been issued in a specific area of Los Angeles County, encompassing 90 industrial firms. An inspector will conduct visits to 30 randomly selected firms to assess compliance with regulations.1. **Problem (a):** - **Question:** If 36 of the firms are actually in violation of at least one regulation, what is the probability mass function (PMF) of the number of firms visited by the inspector that are in violation? - **Options:** - \( \circ \) \( h(x; 30, 0, 4) \) - \( \bullet \) \( h(x; 30, 36, 90) \) - \( \circ \) \( b(x; 30, 0.4) \) - \( \circ \) \( nb(x; 30, 36, 90) \) - \( \circ \) \( b(x; 30, 36, 90) \)2. **Problem (b):** - **Question:** If there are 900 firms in the area, and 360 are in violation, approximate the PMF of part (a) using a simpler PMF. - **Options:** - \( \circ \) \( h(x; 30, 360, 900) \) - \( \circ \) \( h(x; 30, 0.4) \) - \( \bullet \) \( b(x; 30, 0.4) \) - \( \circ \) \( nb(x; 30, 360, 900) \) - \( \circ \) \( h(x; 30, 0.4) \) - \( \circ \) \( b(x; 30, 360, 900) \)3. **Problem (c):** - **Task:** For \( X \) – the number of firms in violation among the 30 inspected out of 900 firms – compute the expected value \( E(X) \) and variance \( V(X) \) for both the exact PMF and the approximating PMF from part (b). (Round your answers to two decimal places.) - **Exact PMF:** - \( E(X) = \_\_\_\_ \) -

Introduction: Denote the random variable X as the number of firms violating at least one of the…

Answered: A second-stage smog alert has been…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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