I don't understand the subscript to the Y, and is ?
It looks like you have a noncentral
I would highly appreciate it if you could help me with this complex problem.
Thanks for your kind assist.
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X has normal distribution , alpha is a determinestic value -different for each sample- and K (number of samples) is too large.
Y is a Random Variable (RV) as X, thus, For each sample there is different Yi. ALPHAs are determinestic values, different for each sampling time and are not equal to Mean value.
Finally, As you mentioned, it may chi-squared distribution we face with.
I need your help urgently.