3. Discrete distributions: bivariatel (a) There is a 390(1) = 0.4 probability to observe X1 = 10 and p(X2) = 0.6 probability to observe X2 = 5. Find the mean and the variance of X. Show work. (b) Based on the joint probability table below, Y, = 10 Y2 = 5 900 X, = 10 0.07 0.33 0.4 X2 = 0.18 0.42 0.6 p(Y) 0.25 0.75 write down the three possible values for the sum of the two variables, X + Y, and the probabilities of observing each value. Show calculation. Check what the probabilities add up to. (c) The variance of Y is a; = 4.6875 and the variance of the sum is of\" = 9.1875. You know the variance of X from (a). Find the covariance, 0'\". Show work