Editing Gamma distribution (section)

===Scaling===
If
<math display=block>X \sim \mathrm{Gamma}(\alpha, \theta),</math>

then, for any {{math|''c'' > 0}},

<math display=block>cX \sim \mathrm{Gamma}(\alpha, c\,\theta),</math> by moment generating functions,

or equivalently, if

<math display=block>X \sim \mathrm{Gamma}\left( \alpha,\lambda \right)</math> (shape-rate parameterization)

<math display=block>cX  \sim \mathrm{Gamma}\left( \alpha, \frac \lambda c \right),</math>

Indeed, we know that if {{mvar|X}} is an [[exponential distribution|exponential r.v.]] with rate {{mvar|λ}}, then {{math|''cX''}} is an exponential r.v. with rate {{math|''λ''/''c''}}; the same thing is valid with Gamma variates (and this can be checked using the [[moment-generating function]], see, e.g.,[http://www.stat.washington.edu/thompson/S341_10/Notes/week4.pdf these notes], 10.4-(ii)): multiplication by a positive constant {{mvar|c}} divides the rate (or, equivalently, multiplies the scale).