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PDF is the probability that a random variable will take a value exactly equal to the random variable, whereas CDF is the probability that a random variable will take a value less than or equal to the random variable.

Let X be a continuous random variable with pdf f and cdf F. By definition, the cdf is found by integrating the pdf: F(x)=x???f(t)dt. By the Fundamental Theorem of Calculus, the pdf can be found by differentiating the cdf: f(x)=ddx[F(x)]

Probability deals with predicting the likelihood of future events, while statistics involves the analysis of the frequency of past events.

The probability density function (PDF) and cumulative distribution function (CDF) help us determine probabilities and ranges of probabilities when data follows a normal distribution. The CDF is the integration, from left to right, of the PDF.

The probability density function (PDF) is a statistical expression that defines the probability that some outcome will occur. In this function, the probability is the percentage of a dataset's distribution that falls between two criteria.

The CDF and PDF are important in probability and statistics for describing random variable behavior. The CDF shows the cumulative probability up to a specific value ?x? (denoted as ?F(x)?), while the PDF displays the probability distribution of a continuous random variable (represented as ?f(x)?).

In summary, PDFs are used to describe the probability of a continuous random variable taking on a certain value, CDFs are used to describe the probability that a random variable (continuous or discrete) will take on a value less than or equal to a certain value, and PMFs are used to describe the probability of a ...