6. [Covariance III] Random variables X1 and X2 represent two observations of a signal corrupted by noise. They have the same mean a\" and variance 02. The signal-to-noiseratio (SNR) of the observation X1 2 or X2 is dened as the ratio SNRX 2 g. A system designer chooses the averaging strategy, whereby she constructs a new random variable S = EgX (a) Show that the SNR of S is twice that of the individual observations, if X1 and X2 are uncorrelated. (b) The system designer notices that the averaging strategy is giving SNRS = (1.5]SNRX. She correctly assumes that the observations X1 and X2 are correlated. Determine the value of the correlation coefcient 9X1,X2- c Under what condition on pp; 3;; can the averaging strategy result in an SNRS that is as 1: 3 high as possible