You have two instruments with which to measure the height of a tower. If the true height is 100 meters, measurements with the first instrument vary with mean 100 meters and standard deviation 1.2 meters. Measurements with the second instrument vary with mean 100 meters and standard deviation 0.85 meter. You make one measurement with each instrument. Your results are X1 for the first and X2 for the second, and are independent. a) To combine two measurements, you might average them, Y=(X1+X2)/2. What are the mean and standard deviation of Y? b) It makes sense to give more weight to the less variable measurement because it is more likely to be close to the truth. Statistical Theory says that to make the standard deviation as small as possible you should weight X2 is very close to half the variance of X1, so X2 should get twice the weight of X1. That is, use W=1/3X1 + 2/3X2 What are the mean and standard deviation of W?