unif[f_] := 1; central[f_] := 6 f (1 - f); 
    broad[f_] := Cosh[3 (f - 1/2)]/(2/3 Sinh[3/2]);

phh = 1; ptt = 1; pht = 1; phtf[f_] := central[f]

<< Graphics`Graphics`

<< Graphics`FilledPlot`

HH[data_] := phh If[MemberQ[data, t], 0, 1]

TT[data_] := ptt If[MemberQ[data, h], 0, 1]

HT[data_] := pht (1/2)^Length[data]

HTFF[data_, f_] := 
      f^Count[data, h] (1 - f)^Count[data, t] phtf[f]

HTF[data_] := Integrate[HTFF[data, f], {f, 0, 1}]

p[data_] := {HH[data], TT[data], HT[data], HTF[data]}

pNorm[data_] := p[data]/Sum[p[data][[i]], {i, 1, 4}]

pNorm[{}] // N

ddata = {h, h, h, t}; ans = pNorm[ddata] // N ;  
    Histogram[ans, FrequencyData -> True]; 
    FilledPlot[HTFF[ddata, f], {f, 0, 1}, Fills -> RGBColor[1, 0, 0], 
      PlotRange -> All]; ans

Integrate[unif[x], {x, 0, 1}]

Integrate[
      central[x], {x, 0, 1}]

Integrate[
      broad[x], {x, 0, 1}]

realBias = 
        Join[Table[h, {i, 1, 35}], Table[t, {i, 1, 35}]];

strongBias = 
        Join[Table[h, {i, 1, 350}], Table[t, {i, 1, 250}]];