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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 = oxy = E[(X − Hx)(Y –Hy)] 3 0.05 0.05 0.2 0.25 Marginal Probability of Distribution of Y a) Complete the table by calculating the marginal probabilities. b) State P (X = 1, Y = 2) c) Calculate P(Y = 4 | X = 2) d) In one sentence, interpret the result you obtained in (c) above. d) 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 = oxy = E[(X − Hx)(Y –Hy)] 3 0.05 0.05 0.2 0.25 Marginal Probability of Distribution of Y a) Complete the table by calculating the marginal probabilities. b) State P (X = 1, Y = 2) c) Calculate P(Y = 4 | X = 2) d) In one sentence, interpret the result you obtained in (c) above. d) Calculate the Cov(X,Y) using the formula 1

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.3: Conditional Probability; Independent Events; Bayes' Theorem
Problem 59E
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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 3 0.1 0.05 0.1 0.05 0.03 0.2 0.02 0.25 oxy = a) Complete the table by calculating the marginal probabilities. b) State P (X= 1, Y = 2) c) Calculate P(Y = 4 | X = 2) d) In one sentence, interpret the result you obtained in (c) above. d) Calculate the Cov(X,Y) using the formula = E[(X − Hx)(Y –Hy)] Marginal Probability of Distribution of Y 1
Transcribed Image Text: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 3 0.1 0.05 0.1 0.05 0.03 0.2 0.02 0.25 oxy = a) Complete the table by calculating the marginal probabilities. b) State P (X= 1, Y = 2) c) Calculate P(Y = 4 | X = 2) d) In one sentence, interpret the result you obtained in (c) above. d) Calculate the Cov(X,Y) using the formula = E[(X − Hx)(Y –Hy)] Marginal Probability of Distribution of Y 1
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