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Option for continuous plot


I have defined the following two functions:

poissonProcess[λ_,n_] := FoldList[Plus,0,Table[-1/λ Log[1-Random[]],{n}]]

showPoissonProcess[λ_,n_,opts___] := With[{pp = poissonProcess[λ,n]},
Show[Graphics[{AbsoluteThickness[1.5],Table[Line[{{pp[[i]],i-1},{pp[[i+1]],i-1}}],{i,1,n}]}],
Axes\[Rule]True,opts]];

for plotting a Poisson process; i.e.,

SeedRandom[1];
showPoissonProcess[4, 20, AspectRatio -> 0.3];

does indeed plot this process. However, I would like to have an option 
that would allow for these horizontal lines to be connected; i.e., 
produce a continuous curve.

Is there a easy way to do this?

Thanks,
V. Stokes


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