Statistics

Question 1

rate parameter lambda

mean or expected value

variance

median

moment

Answer 1

λ is the rate parameter which indicates the average number of events in the given time interval.

The mean or expected value of an exponentially distributed random variable X with rate parameter λ is given by
E[X] = 1/λ = β

The variance of X is given by
Var[X] = 1/λ^2 = β^2

so the standard deviation is equal to the mean

The median of X is given by
m[X] = ln(2)/λ < E[X]

E[X^n] = n!/λ^n

Question 2

exponential distribution

Answer 2

is the probability distribution that describes the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate.