Consider the following random variable...

Consider the following random variable X = /{1, 2} + 2 . 1{3 } + 3 . 1{4, 5, 6} whose distribution function is given by Fx(x) = 0.5 . I{x 2 1} + 0.3 . I {x 2 2} + 0.2 . Ix > 3 }. Construct a probabilitis 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