(2015).
Other related distributions:
Below, suppose random variable X is exponentially distributed with rate parameter original site and

x

1

,

,

x

n

{\displaystyle x_{1},\dotsc ,x_{n}}

are n independent samples from X, with sample mean

a knockout post
x

{\displaystyle {\bar {x}}}

. If

X

1

{\displaystyle X_{1}}

and

X

2

{\displaystyle X_{2}}

are independent exponential random variables with respective rate parameters

1

{\displaystyle \lambda _{1}}

and

2

,

{\displaystyle \lambda _{2},}

then the probability density of

Z
=

X

1

+

X

2

{\displaystyle Z=X_{1}+X_{2}}

is given by
In the case of equal rate parameters, the result is an Erlang distribution with shape 2 and parameter

,

{\displaystyle \lambda ,}

which in turn is a special case of gamma distribution. .

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