Prove that every continuous probability distribution on R, i.e. every probability measure on (R, BR) with...

 

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Prove that every continuous probability distribution on R", i.e. every probability measure on (R", BR) with density w.r.t. the Lebesgue measure in R", is the marginal distribution of a uniform probability distribution on R+1. Hint: Look at the case n = 1 first. Prove that every continuous probability distribution on R", i.e. every probability measure on (R", BR) with density w.r.t. the Lebesgue measure in R", is the marginal distribution of a uniform probability distribution on R+1. Hint: Look at the case n = 1 first.

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Step 12 The statement can be proven using the copula representation of a multivariate distribution A ... View the full answer