p.m. Denote Annie's arrival time by X, Alvie's by Y, and suppose X and Y are ependent with pdf's. What is the expected amount of time that the one who arrives t must wait for the other person? [Hint: h(X,Y)=|X-Y|:] fx(x) = { 3²² fr (x) = { ²0 0≤x≤1 otherwise 0 ≤ y ≤1 otherwise

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Annie and Alvie have agreed to meet for lunch between noon (12:00 p.m.) and
1:00 p.m. Denote Annie's arrival time by X, Alvie's by Y, and suppose X and Y are
independent with pdf's. What is the expected amount of time that the one who arrives
first must wait for the other person? [Hint: h(X, Y)=X-Y|:]
£x(x) = { 31²
0
2y
fr(x) = {2
0≤x≤1
otherwise
0 ≤ y ≤1
otherwise
Transcribed Image Text:Annie and Alvie have agreed to meet for lunch between noon (12:00 p.m.) and 1:00 p.m. Denote Annie's arrival time by X, Alvie's by Y, and suppose X and Y are independent with pdf's. What is the expected amount of time that the one who arrives first must wait for the other person? [Hint: h(X, Y)=X-Y|:] £x(x) = { 31² 0 2y fr(x) = {2 0≤x≤1 otherwise 0 ≤ y ≤1 otherwise
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