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Doug Rivers, professor of Political Sciences in Stanford, kindly sent me this email yesterday night:

The 2nd displayed equation in section 2.1.2 on p. 44 is garbled (it might be interpreted as saying that U and X have the same distribution). I think you intended:

$P(U leq u) = P[F(X) leq u] = P[F^{-1}(F(X)) leq F^{-1}(u)] = P[X leq F^{-1}(u)] = F[F^{-1}(u)] = u$

And indeed we should have stated the implicit convention that u=F(x) before this equation, i.e.

$P(U leq F(x))=P[F(X) leq F(x)]=P[X leq x]=F(x)$

(although U and X cannot be seen to have the same distribution as they live in different spaces).

Filed under: Books, R, Statistics Tagged: Introducing Monte Carlo Methods with R, typos