Q3. Suppose that X and Y are random variables denoting the fraction of a day that a request for merchandise occurs and the receipt of shipment occurs, respectively. The joint probability density function is 1, 0

College Algebra (MindTap Course List)
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Chapter8: Sequences, Series, And Probability
Section8.7: Probability
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Q3. Suppose that X and Y are random variables denoting the fraction of a
day that a request for merchandise occurs and the receipt of shipment
occurs, respectively. The joint probability density function is
1,
0 <x<1, 0<y<1,
f (x, y) =
0,
otherwise.
a) What is the probability that both the request for merchandise and
receipt of an order occur during the first half of the day?
b) What is the probability that a request for merchandise occurs after its
receipt? Before its receipt.
c) Determine the correlation coefficient between X and Y. Comment on the
correlation coefficient.
d) Determine the CDF, F(x,y) of the above probability function.
e) Determine P(0<x<.4, 0.5<x<1).
Transcribed Image Text:Q3. Suppose that X and Y are random variables denoting the fraction of a day that a request for merchandise occurs and the receipt of shipment occurs, respectively. The joint probability density function is 1, 0 <x<1, 0<y<1, f (x, y) = 0, otherwise. a) What is the probability that both the request for merchandise and receipt of an order occur during the first half of the day? b) What is the probability that a request for merchandise occurs after its receipt? Before its receipt. c) Determine the correlation coefficient between X and Y. Comment on the correlation coefficient. d) Determine the CDF, F(x,y) of the above probability function. e) Determine P(0<x<.4, 0.5<x<1).
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