Question: 1.*8. Let X be an arbitrary r.v. with an absolutely continuous distribution. Prove that with probability one the fractional part of X is a normal

1.*8. Let X be an arbitrary r.v. with an absolutely continuous distribution.

Prove that with probability one the fractional part of X is a normal number.

[HINT: Let N be the set of normal numbers and consider g'){X -[X] EN}.]

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