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The formulas for the probability distribution of a continuous random variable are given below: Probability Distribution Function: F(x) = P (X ? x) Probability Density Function: f(x) = d/dx (F(x)) where F(x) = ?x??f(u)du ? ? ? x f ( u ) d u .

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)]

What is the normal distribution formula? For a random variable x, with mean ??? and standard deviation ???, the normal distribution formula is given by: f(x) = (1/?(2??2)) (e[-(x-?)^2]/2?^2).

The general formula for the probability density function (pdf) for the uniform distribution is: f(x) = 1/ (B-A) for A? x ?B. ?A? is the location parameter: The location parameter tells you where the center of the graph is. ?B? is the scale parameter: The scale parameter stretches the graph out on the horizontal axis.

Probability distribution function (pdf): Function for mapping random variables to real numbers. Discrete random variable: Values constitute a finite or countably infinite set.

The Probability Density Function(PDF) defines the probability function representing the density of a continuous random variable lying between a specific range of values. In other words, the probability density function produces the likelihood of values of the continuous random variable.

Poisson Distribution NotationPoisson ( ? )Distributionk = 1,2 , ? ,Pdf? k e ? ? k !Cdf? i = 1 k ? k e ? ? k !Mean?4 more rows

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.