Question

1) Let ?? ∈ {−1,0,1} represet the outcome of games that your favorit soccer team plays; −1 for a loss, 0 for a tie and 1 for a win. Also, let ?? ∈ {0, 1} represent whether the game was played at home (1) or away (0). The following table shows the conditional probability of ??|??: ( picture)

1) Let GE(-1,0,1) represet the outcome of games that your favorit soccer team plays; - 1 for a loss, 0 for a tie and 1 for a win. Also, let H E {0,1} represent whether the game was played at home (1) or away (0). The following table shows the conditional probability of G|H: P(g|h) H 0 0.3 1 0.2 0.3 0.4 0.4 0.4 a. Show whether G and H are independent or not. b. If the proportion of games that the team plays away from home is 50%, find the joint and marginal probability distributions of G and H. P(g.h) 0 p(9) -1 p(h) c. If your team tied their last game, what is the probaility that they played at home?

a. Show whether ?? and ?? are independent or not.

b. If the proportion of games that the team plays away from home is 50%, find the joint and marginal probability distributions of ? and ?.

c. If your team tied their last game, what is the probaility that they played at home?

Answer 1

a).TwO events G and ae sald to be ndepe dent T e fact at one event has occoied does not affect e Pro bab /y Rothe ofe event wl occon The Piobabily that event wll occo, then the tuo events ane satd to be dependent hene we Con see all tRe cond ioral Pro babil "G given Pat has occoned ane non- zeno ne not ndependent event S. Hence G and b). stnce pC Ho) PH)OSf1om the ghen table we can evolucfe the manginal Probabi fiesS P(Gto)- PCHo) PG- HO (0S)x-3) -0.5 P(G-H) P(H) P(G) (0s) x (02) meaginal plG- uS+o : 0.2 P(Go tlo) to)P (Gatlo) (0s)x (o 3) prGott)P) P (otti) (os)x(0u) o.2

manginal pGo) = 0.5t02 035 P (Gto PCHo) P(GHo) = (o-5)x(0u) 0.2 P(G H)= PCH) PCGH) - (o-s) x (o-u) 6.2 maig9 nal PG)- 0-2+0 2 0.4 Again monginal p(Ho) 0-ISt0 5to. moiginal pCH) 0.1+0.2to.2 so,the table can be fled as p(GH) PG) Ho GTI O.IS O-23 G0 0.2 O-35 O-2 G o.2 PCH)

) Prokobyofl phytng at home given tat the tecm las ticd sen by e nvense Probobi ly PH2 Go) P PGo Hp) PCGO) O-31