Let Ω be some basic set, P its probability distribution, and A, B ⊂ Ω events. (1) Show that if A is independent of itself, then P(A) = 0 or P(A) = 1. (2) Show that if A and B are both independent and distinct, then P(A) = 0 or P(B) = 0.
Let Ω be some basic set, P its probability distribution, and A, B ⊂ Ω events. (1) Show that if A is independent of itself, then P(A) = 0 or P(A) = 1. (2) Show that if A and B are both independent and distinct, then P(A) = 0 or P(B) = 0.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Let Ω be some basic set, P its probability distribution, and A, B ⊂ Ω events.
(1) Show that if A is independent of itself, then P(A) = 0 or P(A) = 1.
(2) Show that if A and B are both independent and distinct, then P(A) = 0 or P(B) = 0.
Hint: For the first point, you should think about whether you can solve the equation x = x2, and what this might have to do with the task. In the second, it is worth repeating the definitions of separation and independence, and remembering that P(∅) = 0 (and perhaps the zero product rule).
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