Lebesgue measure, defining random variables

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E Tandril

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Suppose that (Ω, F, P) is Lebesgue measure on the interval [0, 1]


Define random variables X(ω)=ω, Y(ω)=2ω+3 and Z(ω)=4ω+1


Compute P(X < b ∩ Y < c) and P(Z > a) as functions of a, b, c ∈ R
 
E Tandril said:
Suppose that (Ω, F, P) is Lebesgue measure on the interval [0, 1]


Define random variables X(ω)=ω, Y(ω)=2ω+3 and Z(ω)=4ω+1


Compute P(X < b ∩ Y < c) and P(Z > a) as functions of a, b, c ∈ R
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No idea how to start, although from what I understand I think the Lebesgue measure = 1-0 = 1
but that's as far as I can get
 
From what I understand, the Lebesgue measure = 1-0 = 1, however I can't seem to get any further than that, could anyone please help?
Thank you in advance
 
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