Probability density function: \(f(x)=\frac{1}{b-a} \text { for } a \leq X \leq b\) Area to the Left of \(\bf{x}\): \(P(X<x)=(x-a)\left(\frac{1}{b-a}\right)\) Area to the Right of \(\bf{x}\): \(P(X>x)=...Probability density function: \(f(x)=\frac{1}{b-a} \text { for } a \leq X \leq b\) Area to the Left of \(\bf{x}\): \(P(X<x)=(x-a)\left(\frac{1}{b-a}\right)\) Area to the Right of \(\bf{x}\): \(P(X>x)=(b-x)\left(\frac{1}{b-a}\right)\) Area Between \(\bf{c}\) and \(\bf{d}\): \(P(c<X<d)=(d-c)\left(\frac{1}{b-a}\right)\) cdf: \(P(X \leq x) = 1 – e^{(–mx)}\) Poisson probability: \(P(X=x)=\frac{\mu^{x} e^{-\mu}}{x !}\) with mean and variance of \(\mu\)
5.1 Properties of Continuous Probability Density Functions Probability density function (pdf) \(f(x)\): Cumulative distribution function (cdf): \(P(X \leq x)\) 5.2 The Uniform Distribution \(X \sim U ...5.1 Properties of Continuous Probability Density Functions Probability density function (pdf) \(f(x)\): Cumulative distribution function (cdf): \(P(X \leq x)\) 5.2 The Uniform Distribution \(X \sim U (a, b)\) The mean is \(\mu=\frac{a+b}{2}\) The standard deviation is \(\sigma=\sqrt{\frac{(b-a)^{2}}{12}}\) Probability density function: \(f(x)=\frac{1}{b-a} \text { for } a \leq X \leq b\) Area to the Left of \(\bf{x}\): \(P(X<x)> Area to the Right of \(\bf{x}\): \(P(X>x)=(b-x)\left(\frac{1}{b-a}…
