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(a) Find P(X < 0.8). (b) Determine E[X] and Var(X).

(a) Find P(X < 0.8). (b) Determine E[X] and Var(X).

A First Course in Probability (10th Edition)
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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### Problem Statement #### (a) Find \( P(X \leq 0.8) \). #### (b) Determine \( E[X] \) and \( \text{Var}(X) \). ### Explanation - \( P(X \leq 0.8) \) is the probability that a random variable \( X \) takes on a value less than or equal to 0.8. - \( E[X] \) is the expected value of \( X \), representing the mean or average value of the random variable. - \( \text{Var}(X) \) is the variance of \( X \), indicating the degree of spread or dispersion of the random variable's values around the mean.
Transcribed Image Text:### Problem Statement #### (a) Find \( P(X \leq 0.8) \). #### (b) Determine \( E[X] \) and \( \text{Var}(X) \). ### Explanation - \( P(X \leq 0.8) \) is the probability that a random variable \( X \) takes on a value less than or equal to 0.8. - \( E[X] \) is the expected value of \( X \), representing the mean or average value of the random variable. - \( \text{Var}(X) \) is the variance of \( X \), indicating the degree of spread or dispersion of the random variable's values around the mean.
**Problem #3:** Suppose that the random variable \( X \) has the following cumulative distribution function (CDF) shown below. **Graph Explanation:** The graph is a plot of the cumulative distribution function \( F_X \) for a random variable \( X \). - **Axes:** - The horizontal axis (x-axis) represents the values of the random variable \( X \). - The vertical axis (y-axis) indicates the cumulative probability, denoted by \( F_X \). - **Graph Features:** - At \( X = 0 \), the CDF \( F_X \) starts at 0.5. - The CDF is constant at 0.5 from \( X = 0 \) to just before \( X = 1 \). - At \( X = 1 \), the CDF begins to increase linearly. - By \( X = 2 \), the CDF has reached a value of 1.0, where it remains constant. **Figure 1:** CDF \( F_X \)
Transcribed Image Text:**Problem #3:** Suppose that the random variable \( X \) has the following cumulative distribution function (CDF) shown below. **Graph Explanation:** The graph is a plot of the cumulative distribution function \( F_X \) for a random variable \( X \). - **Axes:** - The horizontal axis (x-axis) represents the values of the random variable \( X \). - The vertical axis (y-axis) indicates the cumulative probability, denoted by \( F_X \). - **Graph Features:** - At \( X = 0 \), the CDF \( F_X \) starts at 0.5. - The CDF is constant at 0.5 from \( X = 0 \) to just before \( X = 1 \). - At \( X = 1 \), the CDF begins to increase linearly. - By \( X = 2 \), the CDF has reached a value of 1.0, where it remains constant. **Figure 1:** CDF \( F_X \)
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