MATLAB: Is this correct the correct code for this? Suppose Xi for i=1, 2, 3… has Uniform(0,1) distribution..

math probability statistics computing

Suppose Xi for i=1, 2, 3… has Uniform(0,1) distribution. Let N = min (n+1: Xn > Xn+1). Find E (N) by simulation. 10,000 simulations required.
For the first part I think this is :
S1 = symsum(x, x, 2, inf); %Summation for Xi for i = 2,3,4...
a = 1; %beta distrubtion Uniform(0,1) distribution with a=1 & b=1
b = 1;
data = S1(a,b); %Xi has Uniform(0,1) distribution
N = (S1) > (S1+1) % setting N
if this is correct then i'm only confused on finding E(N) here..
I was horribly off, thank you for the help here

Best Answer

Like John, I have no idea what "min (n+1: Xn > Xn+1)" means, but anyway, is this what you want?
numSimulations = 10; % or 10000
x = rand(1, numSimulations)
% Make "Xn > Xn+1" by sorting in descending order
x = sort(x, 'descend')  % Now Xn > Xn+1 because we sorted it
% Generate a vector of (n+1) values.
nPlus1 = 2 : (length(x) + 1)
N = min([x; nPlus1], [], 1)
% Of course since all x are less than 2, N will equal x.
en = mean(N)
It's also unclear what the difference between n and i. Are they both simply indexes of the arrays? If so, why did you change notation??? Or does n mean something different than i?
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