Overview of basic concepts in Statistics and Probability - SAMSI

Exponential random variables
Overview of
basic concepts
in Statistics
and
Probability
Avanti
Athreya
Preliminaries
Important
distributions,
scaling laws,
and the CLT
Parametric
estimation and
hypothesis
testing
A random variable X is called exponential with parameter λ
(λ > 0) if
P{X > x} = exp(−λx) for all x > 0
Equivalently, an exponential random variable has density
f (x) = λexp(−λx) for x > 0,and 0 elsewhere
Exponential variables have the memoryless property:
P{X > s+t|X > s} =
exp(−λ(s + t))
exp(−λs)
= exp(−λt) = P{X > t}