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# Probability theory, no idea where to start watch

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

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

How do I compute P(X < b ∩ Y < c) and P(Z > a) as functions of a, b, c ∈ R?
2. (Original post by Bruce Harrisface)
Suppose that (Ω, F, P) is Lebesgue measure on the interval [0, 1]

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

How do I compute P(X < b ∩ Y < c) and P(Z > a) as functions of a, b, c ∈ R?
Remember that a random variable is a function . In this case, therefore, X, Y and Z are simply functions .

So to work out , you need to work out what values of satisfy .

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Updated: March 23, 2016
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