No. "theta is a function of the population sample" would be " ".
This appears to say "we have a function, f, of theta, for given values of , , ".
That is, different samples may give different functions of theta, not different theta.
what does the notation
f(theta: Y_1, Y_2.....Y_n) mean?
I believe in this example theta is a parameter of the population sample Y_i.
Does it mean that theta (the parameter itself, say variance or mu) is a function of the population sample? Thanks
No. "theta is a function of the population sample" would be " ".
This appears to say "we have a function, f, of theta, for given values of , , ".
That is, different samples may give different functions of theta, not different theta.