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Find the sum with equations inside

Posted 3 months ago
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Hello, now I try to understand what I want.

Clear["Global`*"]
m = 1;
a = 1/20;
k = 0;
n = 100;
t = {0.7, 0.6, 0, 5};
c = Count[t, {u_, _} /; 1 >= u >= 0];
Y = 1000000;

a = NSolve[
  Sum[PDF[BinomialDistribution[n, p], i], {i, k, m}] == a && 
   1 >= p >= 0, p]
Clear[p]
b = NSolve[
  Sum[PDF[BinomialDistribution[n, p], i], {i, k, m - 1}] == a && 
   1 >= p >= 0, p]
x[m_] = a - b
d = Y*a (m == 0) + 
  Sum[0.7*(a[3] - b[2]) + 0.6 (a[2] - b[1]) + 0.5 (a[1] - b[0]), {i, 
    k, c}]

And I have some questions first 1. According to the first equation,why Nsolve cant find a soulution when a=0.05? When it is 1/20 it works Ok. 2. Why the second Nsolve equation gives empty output in spite of changing the p unkown to another unknown, for example, z?

m and t have direct conection, when m=0 there is no z at al, When m=3 t has three values specified by user. The problem with d that it has another Sum inside and it should use the solutions from a and b depending on m, The sum should be counted by m or t list. In other words, I want d to take values from t list and appropriate solutions from a and b or only a. It should be like this

d = Y*a[0] + 
  Sum[t1*(a[3] - a[2]) + t2 (a[2] - a[1]) + t3 (a[1] - a[0]), {i, k, 
    c}]

But I think it should take solutions into the sum from two ndsolve equations to make it easier.

When you start the calculation, a is a number. After yur first NSolve, a becomes a list of lists of replacement rules.It is not a number any more. You have to extract the numbers inside before feeding them to another NSolve. Have a look at the syntax of NSolve and its solutions, and how you use them.

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