STA 205: Probability & Measure Theory
نویسنده
چکیده
This is sometimes denoted simply “X−1(B) ⊂ F.” Since the probability measure P is only defined on sets F ∈ F, a random variable must satisfy this condition if we are to be able to find the probability Pr[X ∈ B] for each Borel set B, or even if we want to find the distribution function (DF) FX(b) ≡ Pr[X ≤ b] for each rational number b. Note that set-inverses are rather well-behaved functions from one class of sets to another; specifically, for any collection {Aα} ⊂ B,
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