1/3 24. Suppose à2 is the uniform distribution on the unit square [0, 1]2 defined by its distribution function 12([0, 01] x [0, 02]) = 0,02, (91, 02) € [0, 1]². (a) Prove that A2 assigns 0 probability to the boundary of [0, 1]2. (b) Calculate A2{(61, 62) e [0, 1]² : 0 A 02> (c) Calculate d2{(01, 02) E [0, 1] : 01 ^ 02 s x, 01 A O2 sy).

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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24. Suppose A2 is the uniform distribution on the unit square [0, 1]2 defined by
its distribution function
2([0, 01] x [0, 02]) = 0,02, (61, 02) € [0, 1].
(a) Prove that 22 assigns 0 probability to the boundary of [0, 1]2.
(b) Calculate
2{(91, 02) e [0, 1]² : 0, A 02 >
(c) Calculate
À2(91, 02) E [0, 1] : 0 A 02 s x,01 ^ 02 s y).
Transcribed Image Text:24. Suppose A2 is the uniform distribution on the unit square [0, 1]2 defined by its distribution function 2([0, 01] x [0, 02]) = 0,02, (61, 02) € [0, 1]. (a) Prove that 22 assigns 0 probability to the boundary of [0, 1]2. (b) Calculate 2{(91, 02) e [0, 1]² : 0, A 02 > (c) Calculate À2(91, 02) E [0, 1] : 0 A 02 s x,01 ^ 02 s y).
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