Parametrization of the gamma distribution

Some of you have noticed that characteristics (density, expectation, variance etc.) of the gamma distribution in the formula sheet (section 9c) and in our lectures/exercise classes (see e.g. slide 13/27 of Lecture 14) are different. There is no contradiction: the reason is that in the formula sheet they use a different (but equivalent) parametrization.

If, in the formula sheet, you put

beta = 1/lambda

you will obtain exactly what we had during the lectures. In particular, in the formula sheet parametrization, 

E[X] = alpha*beta,

whereas in the parametrization we used during the lectures (and which is more convenient for our course)

E[X] = alpha/lambda.