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## Main Question or Discussion Point

How to prove that a gaussian random variable multiplied by a deterministic sinusoid also results in a random variable with gaussian pdf?

Suppose here A is a guassian random variable and B is given as below where fc is the frequency of sinusoid and t is the time.

B=A∗cos(2π fc t). Is random variable B also gaussian. If so, how to prove it?

This may be a foolish question and/ or direct one . But please help me, I cannot figure it out.

Suppose here A is a guassian random variable and B is given as below where fc is the frequency of sinusoid and t is the time.

B=A∗cos(2π fc t). Is random variable B also gaussian. If so, how to prove it?

This may be a foolish question and/ or direct one . But please help me, I cannot figure it out.