Question: Please find the question below. Suppose X is a continuous random variable defined on a probability space. Let f be the density of X under

Please find the question below. Suppose X is a continuous random variable defined on a probability space. Let f be the density of X under P and assume f > 0. Let g be the density function of a random variable.

EXERCISE 1.6. Suppose X is a continuous random variable dened on a probability space (9,3,1?) Let f be the density of X under 1? and assume f > 0. Let g be the density function of a random variable. Dene Z := g(X)/ f (X) (a) Show that Z E dl~P/d]P denes a Radon-Nikodym derivative. (b) What is the density of X under ll)

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