Let the random variable Y denote the time (in minutes) for which a customer is waiting for the beginning of a service station since its arrival and let X denote the time (minutes) until the service is completed since its arrival at the service station. Since both X and Y measure the time since the arrival of the customer at the service station, always Y

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.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 6E
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Let the random variable Y denote the time (in minutes) for which a customer is waiting for the beginning of a service station since its arrival and let X denote the time (minutes) until the service is completed since its arrival at the service station. Since both X and Y measure the time since the arrival of the customer at the service station, always Y<X is true. The joint probability density function for X and Y is given as follows: 

fxy(x,y)=c(x+y) for 0<x<2 and 0<y<x

what is the value of c? 

what is the covariance of X and Y?

what is the correlation of X and Y? 

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ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,