1. Suppose X1, X2, . . ., X, is a sample from a Normal distribution N (, o) and Y, Y2,..., Y is a sample from a Normal distribution N(, 2). The distributions have the same means but different variances. Assume 0 < 0% 2. You can imagine that two researchers are collecting data from an ex- periment. Researcher X is more careful in their methodology and thus has lower variance in their sample than Researcher Y. We want to understand how to combine the two sets of data to get a good estimate for fl. Define the likelihood in this example to be the product of the likelihoods of the two samples. Using this likelihood, find the MLE for u. Express your solution as a weighted sum of the MLEs for from the individual samples, weighted by terms involving the variances.