Contracts for two construction jobs are randomly assigned toone or more of three

Question

Contracts for two construction jobs are randomly assigned toone or more of three firms, A, B, and C. Let Y1denote the number of contracts assigned to firm A and Y2the number of contracts assigned to firm B. Notice that eachfirm can receive 0, 1, or 2 contracts. The joint probabilityof Y1 and Y2 is given below.                    Y1               Y2         0         1            2 0         1/9      2/9         1/9 1         2/9      2/9         0 2         1/9      0            0 I need to find E(Y1) , V(Y1) , andE(Y1 - Y2). Contracts for two construction jobs are randomly assigned toone or more of three firms, A, B, and C. Let Y1denote the number of contracts assigned to firm A and Y2the number of contracts assigned to firm B. Notice that eachfirm can receive 0, 1, or 2 contracts. The joint probabilityof Y1 and Y2 is given below.                    Y1               Y2         0         1            2 0         1/9      2/9         1/9 1         2/9      2/9         0 2         1/9      0            0 I need to find E(Y1) , V(Y1) , andE(Y1 - Y2). Y2         0         1            2 0         1/9      2/9         1/9 1         2/9      2/9         0 2         1/9      0            0 I need to find E(Y1) , V(Y1) , andE(Y1 - Y2).

Explanation / Answer

Given: Contracts for two construction jobs are randomly assigned toone or more of three firms, A, B, and C. Let Y1denote the number of contracts assigned to firm A and Y2the number of contracts assigned to firm B. Notice that eachfirm can receive 0, 1, or 2 contracts. The joint probabilityof Y1 and Y2 is given below.                    Y1               Y2         0         1            2 0         1/9      2/9         1/9 1         2/9      2/9         0 2         1/9      0            0 Contracts for two construction jobs are randomly assigned toone or more of three firms, A, B, and C. Let Y1denote the number of contracts assigned to firm A and Y2the number of contracts assigned to firm B. Notice that eachfirm can receive 0, 1, or 2 contracts. The joint probabilityof Y1 and Y2 is given below.                    Y1               Y2         0         1            2 0         1/9      2/9         1/9 1         2/9      2/9         0 2         1/9      0            0 Contracts for two construction jobs are randomly assigned toone or more of three firms, A, B, and C. Let Y1denote the number of contracts assigned to firm A and Y2the number of contracts assigned to firm B. Notice that eachfirm can receive 0, 1, or 2 contracts. The joint probabilityof Y1 and Y2 is given below.                    Y1               Y2         0         1            2 0         1/9      2/9         1/9 1         2/9      2/9         0 2         1/9      0            0 Contracts for two construction jobs are randomly assigned toone or more of three firms, A, B, and C. Let Y1denote the number of contracts assigned to firm A and Y2the number of contracts assigned to firm B. Notice that eachfirm can receive 0, 1, or 2 contracts. The joint probabilityof Y1 and Y2 is given below.                    Y1               Y2         0         1            2 0         1/9      2/9         1/9 1         2/9      2/9         0 2         1/9      0            0 Contracts for two construction jobs are randomly assigned toone or more of three firms, A, B, and C. Let Y1denote the number of contracts assigned to firm A and Y2the number of contracts assigned to firm B. Notice that eachfirm can receive 0, 1, or 2 contracts. The joint probabilityof Y1 and Y2 is given below.                    Y1               Y2         0         1            2 0         1/9      2/9         1/9 1         2/9      2/9         0 2         1/9      0            0 Y2         0         1            2 0         1/9      2/9         1/9 1         2/9      2/9         0 2         1/9      0            0 P(Y1 =0) = (1/9)+(2/9)+(1/9) = 4/9 P(Y1 =1) = (2/9)+(2/9)+(0) = 4/9 P(Y1 =2) = (1/9)+(0)+(0) = 1/9 E(Y1 ) =[Y1*P(Y1)] = (0*4/9)+(1*4/9)+(2*1/9) =6/9 V(Y1) =  E(Y1)2 - [E(Y1 )]2 =(02*4/9)+(12*4/9)+(22*1/9)-(6/9)2 = (8/9)-(36/81) = 4/9 P(Y2 =0) = (1/9)+(2/9)+(1/9) = 4/9 P(Y2 =1) = (2/9)+(2/9)+(0) = 4/9 P(Y2 =2) = (1/9)+(0)+(0) = 1/9 E(Y2 ) = [Y2*P(Y2)] =(0*4/9)+(1*4/9)+(2*1/9) = 6/9   E(Y1 -Y2)= E(Y1) -E( Y2) =(6/9)-(6/9) = 0 Hope this helps you P(Y2 =0) = (1/9)+(2/9)+(1/9) = 4/9 P(Y2 =1) = (2/9)+(2/9)+(0) = 4/9 P(Y2 =2) = (1/9)+(0)+(0) = 1/9 E(Y2 ) = [Y2*P(Y2)] =(0*4/9)+(1*4/9)+(2*1/9) = 6/9   E(Y1 -Y2)= E(Y1) -E( Y2) =(6/9)-(6/9) = 0 Hope this helps you Contracts for two construction jobs are randomly assigned toone or more of three firms, A, B, and C. Let Y1denote the number of contracts assigned to firm A and Y2the number of contracts assigned to firm B. Notice that eachfirm can receive 0, 1, or 2 contracts. The joint probabilityof Y1 and Y2 is given below.                    Y1               Y2         0         1            2 0         1/9      2/9         1/9 1         2/9      2/9         0 2         1/9      0            0

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