Question

The following table gives the joint probability distribution between employment status and college graduation among those either employed or looking for work (unemployed). Answer questions 36-40. Non-college grads (Y=0) College grads (Y=1) Total Unemployed X=0) Employed X1 Total 0.024 021120 16 0.105 0.456 0.564 0132 0.868 1.000 Table 2: Joint Distribution of Employment Status and College Graduation 36. Compute E(Y) (a) 0.466 (b) 0.564 (c) 0.946 (d) 0.534 37. Calculate ElYX = 1). (a) 0.456. (b) 0.490 (e) 0.525. (d) 0.946. 38. Calculate E(XY-0). (a) 0.456. (b) 0.945. (c) 0.466. (d) 0.746. 39. A randomly selected member of this population reports being unemployed. What is the probability that this worker is a college graduate? (a) 0.1852 (b) 0.2536 (c) 0.4663 (d) 0.8182 10. Are educational achievement and employment status independient? (a) No. (b) Yes (c) The table does not contain enough information to answer this question (d) Yes, because P(X-0)+PX-1)-1.

Answer 1

Answer 36(b) 0.564 37 (c) 0.525 38 (b) 0.945 39(d) 0.8182 40 (a) No

36 E(Y) = 7 = 0x0.436 + 1 x 0.564 = 0.564 DECYX= 1) = 0 x P(4201X-1) + 1 x PCY=1/x=1) = 0 +1% = 0.525 38) E (xly-o) = 0 *P(x>0} Y-0)+1 * P(=110)-0 +10-412 - o.qus 39 P(y=11x20) = 0.108/0.132 = 0.8182 AD E(X)= 0X0-132 + 1*0.868 = 0.868 , ELY) - 0.564 Vare(x) = 0x0.32 + 1 x0.868-0.868)=0:1146, VaR(Y) = 0²x0.436 + 1² x 0.564-(0.564)² = 0.2459 Com (X,Y)=x0x0024)+(ox)*0.108) + (1xox0.412) + (1*1*0.456)-(0.868x564)=-0.0336 Correlatiem (X,Y)= Cov(x,y)/Jvare(x) Varly) - Toronto zusa -0.1999 Since cov (XY) #0 or Corencelation (x,y) #0, educational achievement and employment status are not independent. Quce

0 Non-college grads (Y = 0) 1 College grads (Y = 1) Total Unemployed (X=0) Employed (X = 1) Total 0.024 0.412 0.436 0.108 0.456 0.564 0.132 0.868 11 E(X) E(Y) E(Y|X=1) = 0 *P(Y=0|X=1) +1*P(Y=1 X=1) E(X|Y=0) = 0 * P(X=0|Y=0) +1* P(X=1 Y=0) PY=1 X=0) Var(x) Var(Y) Cov(XY) Correl(XY) 0.868 0.564 0.525 0.945 0.8182 0.1146 0.2459 -0.0336 -0.1999

The formula view of the calculations as below:

Non-college grads (Y = 0) College grads (Y = 1) Total Unemployed (X = 0) 0.024 0.108 =SUM(C3:04) Employed (X = 1) 0.412 0.456 =SUM(D3:04) Total =SUM(C3:03) =SUM(C4:04) =SUM(C5:05) E(X) E(X) =SUMPRODUCT(C1:01, C5:05) E(Y) =SUMPRODUCT(A3:A4, E3:54) ElY|X=1) = 0 * P(Y=0|X=1) +1* P(Y=1|X=1) =(0*D3/D5)+(1*D4/D5) E(X|Y=0) = 0 * P(X=0|Y=0) +1 * P(X=1|Y=0) =(0*C3/E3)+(1*D3/E3) PIY=1 X=0) =C4/C5 Var(X) =(C1^2*C5)+(D1^2*05)-(C7^2) Var(Y) =(A3^2*E3)+(A4^2*E4)-(C842) Cov(XY) =C1*A3*C3+C1*64*A4+D1*D3*A3+D1*D4*A4-C7*C8 Correl(XY) =C14/(SQRT(C12) *SQRT(C13))