Statistics question: I'm having trouble understanding my statistics professor's objection to this interpretation of confidence intervals. If you have some distribution with parameter x: X = Dist(x), and you perform a random experiment drawing N random variables from it, and derive from those some estimator y related to x, then I *want* to say the following, but my statistics prof insists it's an invalid interpretation: If you have a space with the (unknown) parameter x and the statistic y, for each x there is a conditional probability distribution for the y that will be yielded from a draw of N variables. This leads to a joint probability distribution linking x and y. Now that you have a value for y, you are in a subspace of the space (y=whatever you got), and there is a distribution of probability for x. The probability that you find x within a certain range relates to this distribution. My statistics prof objects that x is a specific value, not a random variable. While I understand that x *in fact* is either within or not within the interval, the best you can give with the imperfect information available is a finite probability. You have limited knowledge due to the statistic y, which is more than no knowledge and less than exact knowledge of what the parameter x is. He insists you cannot make a probability statement about it, and that known confidence intervals don't give you any information about the underlying distribution, only future ones. That x either is or is not within any distribution, and that you cannot say anything about it. (I already understand the point about a certain proportion of future confidence interval draws containing the parameter). I don't know why you can't do this. Can anyone try to enlighten me? Any perspectives you have might help me understand the error.