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Probability theory, no idea where to start

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?

Reply 1

Gregorius

Original post by Bruce Harrisface

Remember that a random variable is a function

\Omega \rightarrow \mathbb{R}

. In this case, therefore, X, Y and Z are simply functions

[0, 1] \rightarrow \mathbb{R}

.

So to work out

P( (X < b) \cap (Y < c))

, you need to work out what values of

\omega \in [0,1]

satisfy

\omega < b \text{ and } 2 \omega + 3 < c

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