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Unformatted text preview: X x 1/2 1 1 y 1/2 1 1 F (y) Y 7. F X ( α ) = P [ X ≤ α ] and F Y ( α ) = P [ Y ≤ α ]. We know that X ( s ) ≤ Y ( s ) for all s ∈ S . Therefore, we can say that Y ( s ) ≤ α implies X ( s ) ≤ α , i.e., the set of all elements s ∈ S such that Y ( s ) ≤ α is a subset of the set of all elements s ∈ S such that X ( s ) ≤ α . { s ∈ S : Y ( s ) ≤ α } ⊂ { s ∈ S : X ( s ) ≤ α } Therefore, we have P { s ∈ S : Y ( s ) ≤ α } ≤ P { s ∈ S : X ( s ) ≤ α } which implies F Y ( α ) ≤ F X ( α ). 2...
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 Spring '11
 TU

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