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8: Parametric Probability Distributions
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Core Algorithms
Improve Manufacturing of LCD Displays
An LCD display is accepted if it has 15 or fewer faulty pixels. Find the maximal pixel fault rate needed to produce
pixel displays and still have an acceptance rate of at least 90%.
In[1]:=
X
prob = Probability[n <= 15, n \[Distributed] PoissonDistribution[4000 2000 \[Lambda]]]
Out[1]=
In[2]:=
X
LogLogPlot[prob, {\[Lambda], 10^7, 10^5}, PlotStyle > Thick, ImageSize > Medium, GridLines > Automatic, Frame > True, BaseStyle > {FontFamily > "Verdana"}, FrameLabel > {Style["Pixel Failure Rate", Bold], None}, PlotLabel > "LCD Acceptance Rate"]
Out[2]=
In[3]:=
X
Maximize[{\[Lambda], prob >= 0.90 && 10^6 < \[Lambda] < 2 10^6}, \[Lambda], Reals]
Out[3]=