plot probability

Question

Hi I just want to flatten a function, I tied it with Joined->True, but it did not work, hope somebody of you can help me.

This is my code:

Remove["Global`*"]
m = 30; (*number of banks*)
n = 5;(*number of defaults*)
AssetV = 100;(*asset value at T*)
DebtV = 80;(*debt value at T*)
μ = 0.2;(*annual drift*)
σ = 0.3;(*annual volatility*)
T = 5;(*years*)
ρ = 0.8;

Since I want to use a BinomialDistribution I calculated the individual probabilities through:

P = (CDF[NormalDistribution[], -(Log[
        AssetV/DebtV] + (μ - 0.5*σ^2)*T)/(σ*Sqrt[
      T])])

In the following I generated a table where I wanted to see the probabilities where k=n1, varies from 0 to 30 since n=30, and this is given by:

data1 = Table[
  Probability[x >= n1, 
   x \[Distributed] BinomialDistribution[30, P]], {n1, 0, 30, 1}]

In order to plot the probabilities I entered:

Plot[Probability[x >= n1, 
  x \[Distributed] BinomialDistribution[30, P]], {n1, 0, 30}, 
 PlotRange -> All, AxesLabel -> {"# of Defaults", "PD"}, 
 Filling -> Axis]

and now I just want to flatten this function. I tried it with Joined-True, which did not work out.

I want also to show the density by:

DiscretePlot[PDF[BinomialDistribution[30, P], n1], {n1, 0, 30}, 
 PlotRange -> All, AxesLabel -> {"# of Defaults", "PD"}, 
 Joined -> True]

However, is there the possibility to implement data1=Table[...] into the two functions, would it be then possible to generate the plot by the ListLinePlot function?

thank you for your help.

Answer 1

You mean like this? (no place to put in comment, will remove if not)

 data = Table[{n1, 
    Probability[x >= n1, 
     x \[Distributed] BinomialDistribution[30, P]]}, {n1, 0, 20}];
ListPlot[data, Joined -> True, Mesh -> True, PlotRange -> All, 
  Frame -> True, PlotStyle -> PointSize[.02], GridLines -> Automatic, 
  GridLinesStyle -> LightGray]

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