Question

Use the probability distribution given in the table below and consider two new random variables, W= 1 + 9X and V = 4 + 2Y, to answer the following questions Joint Distribution of Weather Conditions and Commuting Times Long commute (Y = 0) Short commute (Y = 1) Total Rain (X = 0) 0.04 0.50 0.54 No Rain (X = 1) 0.32 0.14 0.46 Total 0.36 0.64 1.00 Compute the mean of W. E(W) = (Round your response to two decimal places)

Answer 1

xo x=1 120 0.04 0.32 0.36 0.5 0.14 0.64 Yet 0.46 1 o.54 EX) ΣΧΡ(x) OxPlx=0) + IxPlx=11 1X0.46 = 0.46 xo. 46 -0.46 Elx², Ex² plx) = 0 P1x=0) + ² x P (X=1) on? 61x² - LEW) ² = 0.24 84 - 0.64 Eltl = EYP(4) oxPly=0) + 1.P17=1) ElY² = {y² Plil = 0XP14:01 +1 PLT=1 0,²= E(7²) - {Elly² = 0.20 4 -0.64 - 1 + 9x ElW1 = 1 + 9 Elx) 1+gxo.46 5.19 : (Elwl=5.14 4 +27 Elu) 4 + 2x0.64 = 5.28 - 4 + 2 E(1) : Elvl = 5.28 = vli+gx) g2 vixi - 8140.2484 20.1204 = vl 4+24) 2² vly! 4 x 0.230 a 0.9212 CON ( XY) ElXY EIXI EIT oxo . P10,0) + 0x1.P1X20,421) 1.0P(x=1,420) + 1.1. P(X=1,4=1) -0.4680.69 0.14 0.46 Xo 64 = -0.15 49 - CON (x,y) = -0.15 4 4 18x1-0.1544) 18 9x2.coulx,1) - CON (1+9+ 4 +21) CON (u, wl : Coulu, w) = 2.7792 Carr lv,wl= 0.64555 = 8 CON(Nwl σν. σω - -2.7792 0.959791 X 4.4855