Question

1. Consider flipping a fair coin three times and observe whether it lands heads up or tails up. Let X the number of switches from either head to tail or vice versa. For example, when THT is observed, the number of switches is 2 and when HHH is observed, the number of switches is 0. Also, let Y be the number of tails shown in the three times of fipping. (a) List all the values of the joint probability mass function p(x,y) = P(X = x,Y = y).

Answer 1

a) If a fair coin is flipped 3 Hme s men rh e horal, number of elemenary evenrs 13 3 The sample space is HHH, HHT, 14TH, TH1H' TTH, THT/ HTT, Heve X denotes the number of rail or viee versa X hakes he values o,I and 2 y denobes he num ben of haiLs shown in rhe 3 imes of fuppins Pping y takes the valuues o,,2 and 3 o bs errve d

eme HTT is Obsemv ed, obo served. Again, y.. owhen HHH İs observed . , 71, when eiher HHT, HTH y- 2, when eiher HTT,THT Y3, when TTT is o b semved : Thene is no elemev ny evenb for which X-0 and y-

ㄒㄒㄒ THH Nove rhah prroba bi uihy of an event A is P(A)A whe ye nCA) is the numbe of elementamy evenrs favourvble ro A and n is the horal number ofF etementa evenhs. All he n elemena events are equal ikely same way we caleutate he oth e no babi uhes Like f(x=1.Y.-リehe