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Random Processes
Email Arrivals
Assuming email arrivals follow a
PoissonProcess
with a rate of 25 per hour, find the probability that you get no mail for a 15minute period.
In[1]:=
X
emailArrivals = PoissonProcess[25];
In[2]:=
X
Probability[x[0.25] == 0, x \[Distributed] emailArrivals]
Out[2]=
Find the expected number of emails over time.
In[3]:=
X
Mean[emailArrivals[t]]
Out[3]=
Find a 95% confidence band for the expected number of emails.
In[4]:=
X
Plot[{Mean[emailArrivals[t]], Quantile[emailArrivals[t], 0.025], Quantile[emailArrivals[t], 0.975]}, {t, 0, 8}, Filling > {2 > {3}}]
Out[4]=
Simulate the email arrival process for 10 different onehour periods.
In[5]:=
X
RandomFunction[emailArrivals, {0, 1}, 10]
Out[5]=
In[6]:=
X
RandomFunction[emailArrivals, {0, 1}, 10]; ListLinePlot[%, InterpolationOrder > 0]
Out[6]=