A random variable $X$ is said to have an exponential distribution,
$f(x)\ =\ \begin{cases}\lambda e^{-\lambda x}&if\ x>0\\ 0&otherwise\end{cases} $
How can I show that the class of exponentially distributed random variables is closed under multiplication with a positive number
Or in other words, if $X$ is exponentially distributed and $α ∈ (0, ∞)$ how can I show that $ αX$ is also exponentially distributed.