MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Question
--- ### Understanding Response Time and Signal Strength The response time is the speed of page downloads, which is critical for a mobile website. As the response time increases, customers may become frustrated and potentially abandon the site for a competitor. **Variables Defined:** - Let \( X \) represent the number of bars of service. - Let \( Y \) represent the response time (to the nearest second). We define the range of the random variables \( (X, Y) \) as the set of points \( (x, y) \) in two-dimensional space where the probability that \( X = x \) and \( Y = y \) is positive. **Probability Table:** | \( y = \) Response Time (nearest second) | \( x = \) Number of Bars of Signal Strength | Marginal Probability of Distribution of \( Y \) | |---|---|---| | | 1 | 2 | 3 | | | 4 | 0.15 | 0.1 | 0.05 | | | 3 | 0.02 | 0.1 | 0.05 | | | 2 | 0.02 | 0.03 | 0.2 | | | 1 | 0.01 | 0.02 | 0.25 | | | Marginal Probability of Distribution of \( X \) | | | | 1 | --- **Exercises:** a) Calculate \( P(Y = 4 \mid X = 2) \) b) In one sentence, interpret the result you obtained in (c) above. c) Calculate the \( \text{Cov}(X,Y) \) using the formula: \[ \sigma_{XY} = E[(X - \mu_X)(Y - \mu_Y)] \]
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Transcribed Image Text:--- ### Understanding Response Time and Signal Strength The response time is the speed of page downloads, which is critical for a mobile website. As the response time increases, customers may become frustrated and potentially abandon the site for a competitor. **Variables Defined:** - Let \( X \) represent the number of bars of service. - Let \( Y \) represent the response time (to the nearest second). We define the range of the random variables \( (X, Y) \) as the set of points \( (x, y) \) in two-dimensional space where the probability that \( X = x \) and \( Y = y \) is positive. **Probability Table:** | \( y = \) Response Time (nearest second) | \( x = \) Number of Bars of Signal Strength | Marginal Probability of Distribution of \( Y \) | |---|---|---| | | 1 | 2 | 3 | | | 4 | 0.15 | 0.1 | 0.05 | | | 3 | 0.02 | 0.1 | 0.05 | | | 2 | 0.02 | 0.03 | 0.2 | | | 1 | 0.01 | 0.02 | 0.25 | | | Marginal Probability of Distribution of \( X \) | | | | 1 | --- **Exercises:** a) Calculate \( P(Y = 4 \mid X = 2) \) b) In one sentence, interpret the result you obtained in (c) above. c) Calculate the \( \text{Cov}(X,Y) \) using the formula: \[ \sigma_{XY} = E[(X - \mu_X)(Y - \mu_Y)] \]
Expert Solution
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Step 1: Given Information:
Y X Marginal Probability distribution of X
1 2 3
4 0.15 0.1 0.05  
3 0.02 0.1 0.05  
2 0.02 0.03 0.2  
1 0.01 0.02 0.25  
Marginal Probability distribution of X   1

 

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