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Increasing RandomInteger speed

Is there an intelligent way to speed up generating the following
sample from an inhomogeneous Poisson process to be comparable to the
homogeneous one?

mu = RandomReal[10, 10000];

{t1, sp1} = Timing[RandomInteger[PoissonDistribution[#], 1] & /@ mu];
{t2, sp2} = Timing[RandomInteger[PoissonDistribution[10], 10000]];

In[128]:= t1

Out[128]= 8.47253

In[129]:= t2

Out[129]= 0.004


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