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5) Consider the random variable X and Y that represent the number of vehicles that arrive at two separate street corners during a certain 2-minute period. These street corners are fairly close together so it is important that traffic engineers deal with them jointly if necessary. The joint distribution of X and Y is known to be f(x, y) = 9 1 16 4(x+y)' for x = 0, 1, 2,... and y = 0, 1, 2, .... (a) Are the two random variables X and Y indepen- dent? Explain why or why not. (b) What is the probability that during the time pe- riod in question less than 4 vehicles arrive at the two street corners?

5) Consider the random variable X and Y that represent the number of vehicles that arrive at two separate street corners during a certain 2-minute period. These street corners are fairly close together so it is important that traffic engineers deal with them jointly if necessary. The joint distribution of X and Y is known to be f(x, y) = 9 1 16 4(x+y)' for x = 0, 1, 2,... and y = 0, 1, 2, .... (a) Are the two random variables X and Y indepen- dent? Explain why or why not. (b) What is the probability that during the time pe- riod in question less than 4 vehicles arrive at the two street corners?

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
Section12.4: Discrete Random Variables; Applications To Decision Making
Problem 14E
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5) Consider the random variable X and Y that represent the number of vehicles that arrive at two separate street corners during a certain 2-minute period. These street corners are fairly close together so it is important that traffic engineers deal with them jointly if necessary. The joint distribution of X and Y is known to be f(x, y) = 9 16 1 4(x+y)' for x = 0, 1, 2,... and y = 0, 1, 2, .... (a) Are the two random variables X and Y indepen- dent? Explain why or why not. (b) What is the probability that during the time pe- riod in question less than 4 vehicles arrive at the two street corners?
Transcribed Image Text:5) Consider the random variable X and Y that represent the number of vehicles that arrive at two separate street corners during a certain 2-minute period. These street corners are fairly close together so it is important that traffic engineers deal with them jointly if necessary. The joint distribution of X and Y is known to be f(x, y) = 9 16 1 4(x+y)' for x = 0, 1, 2,... and y = 0, 1, 2, .... (a) Are the two random variables X and Y indepen- dent? Explain why or why not. (b) What is the probability that during the time pe- riod in question less than 4 vehicles arrive at the two street corners?
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