1. The response time is the speed of page downloads and it is critical for a mobile Web site. As the response time increases, customers become more frustrated and potentially abandon the site for a competitive one. Let X = the number of bars of service and Y = response time (to the nearest second) We define the range of the random variables (X, Y) to be the set of points (x, y) in two-dimensional space for which the probability that X = X and Y = y is positive. y = Response Time (nearest second) 4 3 2 1 Marginal Probability of Distribution of X x = Number of Bars of Signal Strength 1 0.15 0.02 0.02 0.01 2 0.1 0.1 0.03 0.02 3 0.05 0.05 0.2 0.25 - ©xy = E[(X − #x)(Y → Hy)] Marginal Probability of Distribution of Y a) Calculate P(Y = 4 | X = 2) b) In one sentence, interpret the result you obtained in (c) above. c) Calculate the Cov(X,Y) using the formula 1
1. The response time is the speed of page downloads and it is critical for a mobile Web site. As the response time increases, customers become more frustrated and potentially abandon the site for a competitive one. Let X = the number of bars of service and Y = response time (to the nearest second) We define the range of the random variables (X, Y) to be the set of points (x, y) in two-dimensional space for which the probability that X = X and Y = y is positive. y = Response Time (nearest second) 4 3 2 1 Marginal Probability of Distribution of X x = Number of Bars of Signal Strength 1 0.15 0.02 0.02 0.01 2 0.1 0.1 0.03 0.02 3 0.05 0.05 0.2 0.25 - ©xy = E[(X − #x)(Y → Hy)] Marginal Probability of Distribution of Y a) Calculate P(Y = 4 | X = 2) b) In one sentence, interpret the result you obtained in (c) above. c) Calculate the Cov(X,Y) using the formula 1
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
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:
\[
\sigma_{XY} = E[(X - \mu_X)(Y - \mu_Y)]
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F032f9f2f-4a86-4f7c-abbd-a161821f35fd%2F274c7eaf-9906-472f-b11f-667ca59d70ca%2Ftgd1aw_processed.jpeg&w=3840&q=75)
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
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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