15.2 - Exponential Properties | STAT 414

Here, we present and prove four key properties of an exponential random variable. Theorem Section. The exponential probability density function:. Skiptomaincontent Breadcrumb Home 15 15.2 15.2-ExponentialProperties Here,wepresentandprovefourkeypropertiesofanexponentialrandomvariable. Theorem Section  Theexponentialprobabilitydensityfunction: \(f(x)=\dfrac{1}{\theta}e^{-x/\theta}\) for\(x\ge0\)and\(\theta>0\)isavalidprobabilitydensityfunction. Proof Theorem Section  Themomentgeneratingfunctionofanexponentialrandomvariable\(X\)withparameter\(\theta\)is: \(M(t)=\dfrac{1}{1-\thetat}\) for\(t