# Questions tagged [cumulative-distribution-function]

Cumulative distribution function. While the PDF gives the probability density of each value of a random variable, the CDF (often denoted $F(x)$) gives the probability that the random variable will be less than or equal to a specified value.

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### Correspondence between the "density function of a probability measure" and the "probability density function" (PDF)

Question. If there is a one to one correspondence between a "borel probability measure" on the line $\mathbb{R}$ and a "cumulative distribution function" (CDF) (please see on page ...
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### Why P(X=x) is not zero here?

From the CDF,I feel that the random variable here is continuous.So shouldn't the P(X=x) equals 0 here and we only need to find P(X>=1).
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### Copula Invariance Principle

I don't get why equation 7 is true, can someone explain me why? This is part of the proof of the invariance principle in copula theory.
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