A random variable Y is defined to be the difference between the higher value and the lower value when two dice (X1, X2) are thrown. If the two dice have the same value, Y is defined to be zero. . Find the probability distribution for Y . Calculate the expected value of Y . Calculate the expected value of Y2 . Compute the expected value of Y given that X1 > 3. . Calculate the variance of Y . Consider Y = 3X + 10. Calculate the possible values of Y. . Compute the expected value and variance of Y.The following table gives the joint probability distribution between employment. status and college graduation among those that are either employed or unemployed in the working-age population of a given country Unemployed (Y=0) Employed (Y=1) Total Non-College graduates [X = 0} 0.030 0.002 0.038 College graduates {X = 1) 0.010 0.352 0.302 Total | 0.040 0.954 1.000 0 Compute E {Y} a Show that E ( Y] = P0\" = 1} for a dummy variable (rt-2 with possible outcomes 0 or 1]. Problem 5 2 c The unemployment. rate is the fraction of the labor force that is unemployed. Conclude from the previous question that it is equal here to 1 EU\"). 0 Calculate E(Y|X = 1) and E{Y|X = 0) o Are educational achievement. and employment status independent '3 Explain