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14. Let (2, F, P) be a probability space on 2 = (0, 1) with F = B(0,1) and P the Lebesgue measure. let A=(;,) and B = (0, ?) a) Are A and B Lebesgue measurable ? Why ? b) If they are Lebesgue Measurable, what are P(A) and P(B)? Why? c) If A and B are Lebesgue measurable, are they independent events? Give reasons for your answer.

14. Let (2, F, P) be a probability space on 2 = (0, 1) with F = B(0,1) and P the Lebesgue measure. let A=(;,) and B = (0, ?) a) Are A and B Lebesgue measurable ? Why ? b) If they are Lebesgue Measurable, what are P(A) and P(B)? Why? c) If A and B are Lebesgue measurable, are they independent events? Give reasons for your answer.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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14. Let (2, F, P) be a probability space on 2 = (0, 1) with F = B(0,1) and P the Lebesgue measure. let A = (;, 3) and B = (0, ?) a) Are A and B Lebesgue measurable ? Why ? b) If they are Lebesgue Measurable, what are P(A) and P(B)? Why? c) If A and B are Lebesgue measurable, are they independent events? Give reasons for your answer.
Transcribed Image Text:14. Let (2, F, P) be a probability space on 2 = (0, 1) with F = B(0,1) and P the Lebesgue measure. let A = (;, 3) and B = (0, ?) a) Are A and B Lebesgue measurable ? Why ? b) If they are Lebesgue Measurable, what are P(A) and P(B)? Why? c) If A and B are Lebesgue measurable, are they independent events? Give reasons for your answer.
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