cumulative density function

You might recall, for discrete random variables, that F ( x) is, in general, a non-decreasing step function. Many questions and computations about probability distribution functions are convenient to rephrase or perform in terms of CDFs, e.g. Using this definition, one can write the probability that XXX takes a value in a certain interval [a,b][a,b][a,b] without using an integral. It gives the probability of finding the random variable at a value less than or equal to a given cutoff. Sign up to read all wikis and quizzes in math, science, and engineering topics. Since the CDF corresponds to the integral of the PDF, the PDF corresponds to the derivative of the CDF: fX(x)=FX′(x)=dFXdx.f_X(x) = F_X'(x) = \frac{dF_X}{dx} .fX​(x)=FX′​(x)=dxdFX​​. It gives the probability of finding the random variable at a value less than or equal to a given cutoff. Recall that previously this probability was defined in terms of a PDF: P(a≤X≤b)=∫abfX(x) dx.P(a\leq X \leq b) = \int_a^b f_X (x) \,dx.P(a≤X≤b)=∫ab​fX​(x)dx. for \(0

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