# plotting cumulative distribution function

c = 2;
P = N[n*Log[n]]
K = N[c*Log[n]]

Needs["PlotLegends"];

PrDEqK[P_, K_, n_, c_, k_] := Module[{p, q, r, ps, qs, m, tmp},
r = Sqrt[(c*Log[n])/(n*\[Pi])];
p = \[Pi]*r^2;
q = 1 - p;
ps = 1 - Binomial[P - K, K]/Binomial[P, K];
qs = 1 - ps;

N[Sum[Binomial[n - 1, m]*p^m*q^(n - 1 - m)*Binomial[m, k]*ps^k*
qs^(m - k), {m, k, n - 1}]]

];
Plot[CDF[{PrDEqK[P, K, 20, c, k], {k, 1, 8},Filling -> Axis
]


i'm not getting the CDF plot...what is the problem?

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CDF, for one thing, is for distributions, you are trying to plot a function. There are other issues with the code, please attempt to fix these and add some context to the question. –  ciao Jan 17 '14 at 8:39

As has been CDF acts on distribution objects. You have defined a discrete PMF. With all due respect the plot by Boson is not a CDF but a continous plot of PMF.

Reproduing user-defined:

c = 2;
n = 20;
P = N[n*Log[n]];
K = N[c*Log[n]];

PrDEqK[P_, K_, n_, c_, k_] :=
Module[{p, q, r, ps, qs, m, tmp}, r = Sqrt[(c*Log[n])/(n*\[Pi])];
p = \[Pi]*r^2;
q = 1 - p;
ps = 1 - Binomial[P - K, K]/Binomial[P, K];
qs = 1 - ps;
N[Sum[Binomial[n - 1, m]*p^m*q^(n - 1 - m)*Binomial[m, k]*ps^k*
qs^(m - k), {m, k, n - 1}]]];


To generate CDF:

cdf[k_] := Sum[PrDEqK[P, K, 20, c, j], {j, 0, k}];


Visualizing:

DiscretePlot[cdf[k], {k, 0, 8}]


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thank you all... –  user11609 Jan 17 '14 at 9:39
can we plot this CDF combinedly for different values of 'n'that i fixed to 20.. –  user11609 Jan 17 '14 at 11:13
@user11609 yes. Just redefine function to:cdfgeneral[n_,k_]:=Sum[PrDEqK[P, K, n, c, j], {j, 0, k}]; –  ubpdqn Jan 17 '14 at 11:16
okk...thank u so much.. –  user11609 Jan 17 '14 at 11:20

I tried to clean your code a little and it worked right away:

c = 2;
n = 20;
P = N[n*Log[n]];
K = N[c*Log[n]];

PrDEqK[P_, K_, n_, c_, k_] :=
Module[{p, q, r, ps, qs, m, tmp}, r = Sqrt[(c*Log[n])/(n*\[Pi])];
p = \[Pi]*r^2;
q = 1 - p;
ps = 1 - Binomial[P - K, K]/Binomial[P, K];
qs = 1 - ps;
N[Sum[Binomial[n - 1, m]*p^m*q^(n - 1 - m)*Binomial[m, k]*ps^k*
qs^(m - k), {m, k, n - 1}]]];

Plot[PrDEqK[P, K, n, c, k], {k, 1, 8}, Filling -> Axis]
`

EDIT: I am sorry, I have not read the question thoroughly and did not notice you wanted a CDF. ubpdqn is absolutly right.

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