Built-in Statistical Distributions
Mathematica has built-in support for continuous and discrete statistical distributions. This plots the Weibull distribution for several parameter values.
In[1]:=  |  Plot[Evaluate[
Table[PDF[WeibullDistribution[\[Alpha], 1]][x], {\[Alpha], 5}]], {x,
0, 2}, Filling -> Axis, Frame -> True] |
Out[1]=  |  |