Question: Consider the following random variable X = I{1,2}+2. I{3}+3. I{4, 5, 6} whose distribution function is given by Fx(x) = 0.5 I{x > 1}

Consider the following random variable X = I{1,2}+2. I{3}+3. I{4, 5, 6} whose distribution function is given by Fx(x) = 0.5 I{x > 1} +0.3 I{x 2} +0.2 I{x 3}. Construct a probabilitiy space that induces the above distribution. In par- ticular, obtain the o-field generated by X, which is the smallest among all o-fields that makes X a random variable.

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