Exponential distribution

The exponential distribution is a class of probability distribution defined by a decaying exponential function. Its probability density function is given by:

$$f_X(x)=\{\begin{array}{ll}0& x<0\\ \lambda e^{-\lambda x}& x\ge 0\end{array}$$

And its cumulative distribution function is given by:

$$F_X(x)=\{\begin{array}{ll}0& x<0\\ 1-e^{-\lambda x}& x\ge 0\end{array}$$

Computations

The expected value is given by:

$$E(X)=\frac{1}{\lambda }$$

The variance is given by:

$$\text{Var}(X)=\frac{1}{{\lambda }^2}$$

The characteristic function is given by:

$${\Phi }_X(\omega )=$$