Is this is an obvious or tricky question?

#1
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!
 
#2
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
 
#3
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
#4
I'm not sure what your implying when saying there could be more valid answers. That seems like the "correct" answer to me.
 
#5
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.