Unformatted text preview: both 1 / 2. Find the most probable number of boys and girls in the family, and the corresponding probability. 6. Composition of measurable maps. Prove that a composition of two measurable maps is measurable. 7. Random variables induce probability measures on R Let X be a random variable on a probability space (Ω , F , P ). Prove that X induces a probability measure on R in the following sense. For every Borel subset A of R , de±ne P ( A ) := P ( X ∈ A ) = P ( ω ∈ Ω : X ( ω ) ∈ A ) . Prove that ( R , R ,P ) is a probability space....
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- Probability, Probability theory, Probability space, Borel