# Question:superimposed normalized distribution function / PDF algebra

## Question:superimposed normalized distribution function / PDF algebra

Maple

My problem is in statistics. I'm looking for the resulting normalized distribution funtion.

Given a sample has a normal distribution of trait A, and given a subgroup that posseses trait B with a different normal distribution of trait A. Waht would the distribution of trait A be if we eliminate the subgroup that posseses trait B.

The following example that assumes a subgroup of 20% does not yield the proper result.

N:=RandomVariable(Normal(100,15)); # normal distribution of trait A in the whole sample
M:=RandomVariable(Normal(80,15));  # normal distribution of trait A in the subgroup that also posseses trait B
f_1:=t->PDF(N,t);
f_2:=t->PDF(M,t);
f_g:=t->((0.8*f_1(t))-(0.2*f_2(t)));
Apx:=plot(f_1(x),x=0..K);
Bpx:=plot(f_2(x),x=0..K);
Cpx:=plot(f_g(x),x=0..K);
plots[display](Apx,Bpx,Cpx);

My idea for a solution:
1. transform the normalized distribution in one that represents the real number of members.
2. substract the real number of members in the subgroup from the whole sample.
3. normalize the result agin.

But, I have no idea how to accomplish this in Maple.

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