5. (a) [14 POINTS] Let X and Y be two independently distributed random variables with variances V (X) = of and V (Y ) = ov, and standard deviations ox = 4 and or - 3. Compute the standard deviation of X + Y. (b) [15 POINTS] Let X; be a random variable that may take value 0 or 1, with P (X, - 0) - 0.5. (i) What is the distribution of X,? (ii) Let S3 = _Xi, What is the distribution of S3? (iii) Compute P (S3 { 1)