### Quiz Analysis using Joint PMF#### IntroductionAn instructor has given a short quiz consisting of two parts. For a randomly selected student, let \( X \) represent the number of points earned on the 1st part of the quiz and \( Y \) represent the number of points earned on the 2nd part. The joint probability mass function (pmf) of \( X \) and \( Y \) is provided in the following table:#### Joint PMF Table\[ p_{XY}(x, y) \]| \( X \backslash Y \) | 0 | 5 | 10 | 15 ||---|------|------|------|------|| 0 | 0.02 | 0.06 | 0.02 | 0.1 || 5 | 0.04 | 0.15 | 0.2 | 0.1 || 10| 0.01 | 0.15 | 0.14 | 0.01 |### Questions and Solutionsa. **Expected Total Recorded Score \( E[X + Y] \):** - Compute the expected value of \( X + Y \) by calculating \( E[X] \) and \( E[Y] \), then summing them up. b. **Covariance Between \( X \) and \( Y \):** - Compute the covariance to understand how \( X \) and \( Y \) vary together. c. **Correlation Coefficient \( \rho_{XY} \):** - Calculate the correlation coefficient to measure the strength and direction of the linear relationship between \( X \) and \( Y \).d. **Association Between \( X \) and \( Y \):** - Analyze whether there is an association between the number of points earned on the two parts of the quiz and explain the reasoning. ### Detailed Steps for Solution:**1. Expected Value of X and Y:** \[ E[X] = \sum_{x} x \times P(X=x) \] Calculate the marginal probability for \( X \) and \( Y \) and compute their expected values. **2. Expected Value of X + Y:** \[ E[X+Y] = E[X] + E[Y] \] **3. Computing Covariance \(

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Answered: An Instructor has given a short quiz…

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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