Consider the sample space = {H,T}, representing all possible outcomes of 3 coin tosses. Consider the...

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Consider the sample space = {H,T}³, representing all possible outcomes of 3 coin tosses. Consider the function X: 2 → R given by X(w) = 5 4 5 2 if @₁ = H and @3 = H, = if @₁ H and 3 = T, T and 3 = H, if @₁ = if @₁ = = T and @3=T. Is X measurable with respect to the o-algebra generated by the set {w EN: 03 = H}? If yes, argue why. If no, describe how you would modify the value of X in exactly one clause in the definition above to make it measurable. Consider the sample space = {H,T}³, representing all possible outcomes of 3 coin tosses. Consider the function X: 2 → R given by X(w) = 5 4 5 2 if @₁ = H and @3 = H, = if @₁ H and 3 = T, T and 3 = H, if @₁ = if @₁ = = T and @3=T. Is X measurable with respect to the o-algebra generated by the set {w EN: 03 = H}? If yes, argue why. If no, describe how you would modify the value of X in exactly one clause in the definition above to make it measurable.