## Question

You can use this example:

X= number of total active users out of number of total users.

Y=number of total users

Y=D1*625 and D1 can take integer values 1,2,3,4,5,6,7,8,9,10. For example, the maximum total users is 625*10. The maximum number will change with the distribution type and probability. For constant case, we can take Y=6250 when probability(p) is equal to 1, but if it is binomial and the probability is equal to 0.1 then Y=625*2, if it is 0.2 then Y=2*625.

## Solution Preview

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% Assume Y_max=6250Y_max=100;%6250;

% Assume Y has a binomial distribution with parameter Y_max, p1=.1;

p1=.1;

% Assume X|Y has a binomial distribution with parameter Y, and p2=.2;

p2=.2;

%distribution of X f(x)=sum_y f(x|y)f(y)

f_X=zeros(Y_max+1,1);

f_XY=zeros(Y_max+1,Y_max+1);

for y=0:Y_max

p_y=binopdf(y,Y_max,p1);

for x=0:y

f_XY(x+1,y+1)=binopdf(x,y,p2)*p_y;...

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