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13 15 13 6. A jar of marbles has 52 marbles, colored red, green, blue, and yellow. There are 13 of each color. Two marbles are selected at random, with replacement. Let the random variable X be the number of red marbles selected. Construct the probability mass function and cumulative distribution function. Use the table to report your answers. f(x) F(x)

13 15 13 6. A jar of marbles has 52 marbles, colored red, green, blue, and yellow. There are 13 of each color. Two marbles are selected at random, with replacement. Let the random variable X be the number of red marbles selected. Construct the probability mass function and cumulative distribution function. Use the table to report your answers. f(x) F(x)

MATLAB: An Introduction with Applications
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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**Title: Probability Distribution of Red Marbles Selected from a Jar** **Problem Statement:** A jar contains 52 marbles, distributed equally among four colors: red, green, blue, and yellow, with 13 marbles of each color. Two marbles are selected at random with replacement. Define the random variable \( X \) as the number of red marbles selected. Construct the probability mass function (PMF) and cumulative distribution function (CDF) using the table provided to report your answers. **Table Layout:** The table consists of three columns labeled \( x \), \( f(x) \), and \( F(x) \), intended to represent the number of red marbles selected, the probability mass function, and the cumulative distribution function, respectively. The rows in the table indicate possible outcomes for selecting 0, 1, or 2 red marbles. **Explanation of Table:** - **Column \( x \):** Represents the number of red marbles chosen (0, 1, or 2). - **Column \( f(x) \):** Represents the probability of selecting \( x \) red marbles (PMF). - **Column \( F(x) \):** Represents the cumulative probability of selecting up to \( x \) red marbles (CDF). This exercise helps in understanding discrete probability distributions and how to build PMFs and CDFs for random variables based on given scenarios.
Transcribed Image Text:**Title: Probability Distribution of Red Marbles Selected from a Jar** **Problem Statement:** A jar contains 52 marbles, distributed equally among four colors: red, green, blue, and yellow, with 13 marbles of each color. Two marbles are selected at random with replacement. Define the random variable \( X \) as the number of red marbles selected. Construct the probability mass function (PMF) and cumulative distribution function (CDF) using the table provided to report your answers. **Table Layout:** The table consists of three columns labeled \( x \), \( f(x) \), and \( F(x) \), intended to represent the number of red marbles selected, the probability mass function, and the cumulative distribution function, respectively. The rows in the table indicate possible outcomes for selecting 0, 1, or 2 red marbles. **Explanation of Table:** - **Column \( x \):** Represents the number of red marbles chosen (0, 1, or 2). - **Column \( f(x) \):** Represents the probability of selecting \( x \) red marbles (PMF). - **Column \( F(x) \):** Represents the cumulative probability of selecting up to \( x \) red marbles (CDF). This exercise helps in understanding discrete probability distributions and how to build PMFs and CDFs for random variables based on given scenarios.
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