An unknown but fixed voltage v is measured using 3 different sensors. The 3 measurements. X1, X2 and X3, are as follows: X1=v+N; X2= v+N2; X3 = v+ N3, where N1, N2, Na are iid Gaussian variables with zero mean and variance 1. (Note that v is a constant.) (a) (7 points) Find the joint pdf of X1, X2, X3. (b) (6 points) Find the marginal pdf of X1. Are the 3 measurements independent? (c) (7 points) Find the probability that at least 2 of the 3 measurements are greater than v