3. Discrete distributions: bivariate (a) There is a p(X1) = 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, Y1 = 10 Yz = 5 p(X) X1 = 10 0.07 0.33 0.4 X2 = 5 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 oy = 4.6875 and the variance of the sum is orty = 9.1875. You know the variance of X from (a). Find the covariance, Oxy. Show work