Question: 4. Let ? be the sample space of a two coin toss experiment. Suppose our o-algebra is given by F = 10, 0, {HH, TT}

4. Let ? be the sample space of a two coin toss experiment. Suppose our o-algebra is given by F = 10, 0, {HH, TT} {HT, TH} }. Let the functions X : 0 - R and Y : 0 - R be defined by 1 if we {HT} 1 if we {TH}, X(w) = 0 if we {HH, TT, TH} Y(w) = 0 if we {HH, TT, HT} a. Is X a random variable? why or why not? b. Is Y a random variable? why or why not? c. Find Z = max(X, Y). Is Z a random variable? why or why not

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