Two machines produce rivets for a factory job. The number of sub-standard rivets per hour by the two machines are random variables, denoted by X1 and X2

Problem 1 Two machines produce rivets for a factory job. The number of sub-standard rivets per hour by the two machines are random variables, denoted by X; and X3. The bivariate PM? of X1 and X3, px1X1 (x1, x2) , is given in the table below. X2=0 X2=1 X2=2 X2=3 X1 =0 0 07 0.05 0 02 0 01 X1 = 1 005 016 0.12 002 X1=2 002 012 017 005 X1 = 3 001 001 0.05 007 (a) Derive and plot the marginal PMFs of random variables X1 and X2, i.e._. p};1 (X1) and pX: (X2) . (b) Compute the mean and variance of X2. (c) Determine and plot the conditional PMFs pX2 X1 (X2 | x!) . (d) Compute the conditional mean of X2 given X1, \"*lex1 = E [X2 | X1] . Then take the expected value X2 31 of \"X231 with respect to X1, EX1 [axial] to find the unconditional mean of X2, 0X1 . Compare with your result in part (b)