Is this is an obvious or tricky question?

curiosity_the_cat

New Member
Suppose I have two distributions, N(0,1) and N(1,1), and I pick one with half probability.

Then, I take a draw, and observe it is equal to 0.7.

Is there a way to calculate the probability that it was generated by one distribution or the other?

Thanks!

katxt

Member
Work out the height of each normal graph at x = 0.7 The likelihood of each distribution is proportional to the heights of the graphs.
=NORMDIST(0.7,0,1,0) and =NORMDIST(0.7,1,1,0) in Excel

curiosity_the_cat

New Member
Thanks. I figured it out at some point, and I'm impressed you answered with an Excel example!

I'm not sure it's the only valid answer (lack of conditionals uniqueness), but it's certainly the most intuitive!

Thanks again.

Dason

Ambassador to the humans
I'm not sure what your implying when saying there could be more valid answers. That seems like the "correct" answer to me.

curiosity_the_cat

New Member
This is definitely correct. Sometimes conditional pdf's are not unique, and so I wonder if that would apply here. (i.e., does the Borel paradox have any bearing here?) But I'm quite happy with the answer, yes.