Question

The following table gives the joint probability distribution between employment status and college graduation among those either employed or looking for work (unemployed) in the working age U.S. population Unemployed (Y-0) 0.0426 0.0103 0.0529 Employed Non-college grads (X- 0) College grads (X= 1) Total 0.6248 0.3223 0.947 Total 0.6674 0.3326 0.9999 The expected value of Y, denoted E(Y), is. (Round your response to three decimal places.) The unemployment rate is the fraction of the labor force that is unemployed. Show that the unemployment rate is given by 1-E(Y) Unemployment rate11 E(Y)1-0.947 0.0529 E(Y X = 1) is . (Round your response to three decimal places.) E(Y| X-0) is. (Round your response to three decimal places.) The unemployment rate for college graduates is and the unemployment rate for non-college graduates is (Round your responses to three decimal places.) A randomly selected member of this population reports being unemployed. The probability that this worker is a college graduate is, and the probability that this worker is a non-college graduate is [. (Round your responses to three decimal places.) Are educational achievement and employment status independent? 0 A. Since Pr (X=0 | Y= 1)* Pr (X= 0), educational achievement and employment status are not independent O B. Since Pr (X 0, Y 1) Pr (X 0), educational achievement and employment status are not independent ° C. Since Pr (X= 0, Y= 1) = Pr (X= 0), educational achievement and employment status are independent. O D. Since Pr (X-0lY 1) Pr (X-0), educational achievement and employment status are independent

Answer 1

Date Farom the aloove table we get Px-o, Yo) 0 0426 P (x=o,Y-1) = 0.6248 PCX = o) =0.6674 "(x=1) = 0. 3326 p (xzt,Y-1) = 0.3223. P(Y-1) .947. = -oto947 ニ o. 947. Un employmom t Rola, 1-E(Y)-=-1-0.947=0.0529

P CY= 1, x = 1) - O3 223 PC A O 33 26 PCB) 0:969 o,"6243 0.6674 0,936 =

unemployment So Unomploy ment ab moo rate = 0.0529 College xadluale O10 ment nal aduales043 PCe) Comi Hond pababilihy indapendlent = p(A) 囱 Since, Pa(X.olr.4)-..土.P(Xeo), eelucstionol achisvement amdl ammployment Statup are not inedepemdlent