Consider the following code:
f[b_] = ProbabilityDistribution[ b Exp[-bx] , {x, 0.01, \[Infinity]}, Assumptions -> b > 0]; Plot[PDF[f[1.5], x], {x, 0, 2}, PlotRange -> All]
Thank You Hans Milton. It works
I think you are missing a space between b and x in -bx. Or an explicit multiplication operator.
f[b_] = ProbabilityDistribution[b Exp[-b*x], {x, 0.01, \[Infinity]}, Assumptions -> b > 0]; Plot[PDF[f[1.5], x], {x, 0, 2}]