Question

Question Use the probability distribution given in the table below to answer the following questions Joint Distribution of Weather Conditions and Commuting Times Rain (X 0) No Rain (X 1) Total Long commute (Y 0) Short commute (Y 1) 0.26 0.13 0.39 0.58 0.03 0.61 Total 0.84 0.16 1.00 Compute the mean of Y E (Y) (Round your response to two decimal places) Compute the mean of X E (X) (Round your response to two decimal places) Compute the variance of X. Enter your answer in each of the answer boxes.

Answer 1

fyly) X=1 Total 0.39 0.61 0-13 1.00 Y=0 x=0 0.26 0.58 0.84 0.03 0.16 x(x) Total E(Y)= y. fy (4) - 0 (0:39) + 1.60-61) = 0.6) F(x )= E(X). n. fx (x) 0 (0.84) + 1 (0.16 20:16 E ECX 2) - LE CX)] E (X²) = { x fx lx) -0.60.84) + (0:16) = 0.16

54 E(Y) - [E(y)] ² Ec4?). {y' furly - 01039) 06) Icoon C 0.16- (0.16) - - 0.16 0.0256 - 01344 = - - 0.61 – 10.612 0.61 -0.3721 0.2379 coro (xiv) - Coucx,y) Juance) - Juarly) Coulx, y) = E(XY) - E(X) ECY) ECXV) - 0.0 + (0:26) + 0.1.10.13) + 1.0.10 1.), (0.03) - 0.03

COUCXY) 0.03- co. 16) (061) 0.03 0.0976 -0.0676 cors (x, y) = = 0.0076 C0.3666).(0.7810) - 0.0676 0.28 63146 = -0.2361 AXY OVA ECY) = 0.61 E(X) = 0.16 87 0.1344 07 0.2379 cour(x, y) = – 0.2361