CDF of a random variable X follows a uniform distribution

In the first weekโ€™s assignment, it is given โ€œIn the lectures, you learned that if ๐‘‹ is a random variable with cdf ๐น, then ๐น(๐‘‹) follows a uniform distribution between 0 and 1. In other words, the new random variable ๐น(๐‘‹) will be uniformly distributed between 0 and 1โ€.

What might be the reasoning behind this statement?

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I recommend you watch carefully the video โ€œSampling from a distributionโ€ again.

I also frowned when I read this paragraph which doesnโ€™t seem logical at first. But returning to the video I finally could understand it and realize such an outstanding mathematical property.