Question: Let (0, F, P) be a probability space and X : 0 - R be a random variable. Denote the Borel o-algebra on R as

Let (0, F, P) be a probability space and X : 0 - R be a random variable. Denote the Borel o-algebra on R as B(R), and define the function Mx (B) = P(X-'(B)) for all B E B(R). Show that (R, B(R), Mx) is a probability space. Hint: Use the fact that P is a probability measure and the definition of a random variable. [2]

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2. The purpose of the acquisition of the information.

1. What is the meaning of the information we are collecting?

3. How much information do we need to collect?