Let X be a random variable with mean [tex]\mu[/tex] and standard deviation 1. Let's add a twist. Suppose [tex]\mu[/tex] is randomly distributed about 0 with standard deviation 1. At each iteration, we select a new [tex]\mu[/tex] according to its distributuion. This mean is then used in the distribution for X. Then we pick an X according to its distribution. My question: What is the resulting joint distribution? Given this joint distribution, I should be able to calculate the mean and standard deviation. Clearly, the mean X will be 0, but what will be the standard deviation of X? It seems that it should, at a minimum, be greater than 1. Thanks!