Question

6- (15%) Assume that X=The final grade of a student in Stochastic Modeling class and Y=The final grade of a student in Structural Analysis class The joint probability of the grades earned by a student is P(X,Y) which is as follows. Stochastic Modeling Grades Structural Analysis Grades 95 0.2 0.3 90 75 80 0.4 0.1 How the grades of Stochastic and Structural Analysis classes are related to each other? (Positive. Negative or no relationship?) *Hint: No need for the final value of p. Do necessary calculations to show how X and Y are related to each other (Positive, Negative or no relationship)

Answer 1

Ef suctural 95 75 0.4 0.4 Stochastic go Modeling Grades 75 0.4 0.5 Marginal pmf of a Analysis Grades 80 Total pol 0.6 0.2 0.6 Marginal ponf of y 0.3 Y 95 Total 0.5 Plys 0.5 EXS = Explus 90 (0.65 +75(0.4) = 84 £(7) - Ey P (I) 95(0.5) +80 (0:5) = 87.5. E(XY) = {Eny Ple, y) = gox gsxo.2 goxloxory + 75x95 X0.3 + 75x80x0,9 = 7327.5 Cov(x,y) = E(XY) EK45 – Eks. Elus = 7327.5 84x87.5 --22.5 Since Covariance of X and Y is negative, so the grades of Stochastic and Structural Analysis classes negatively related to each other.