# Estimate the Induction Time Distribution for a Disease

#### Create a kernel density estimate of the AIDS induction time distribution and compute its mean.

 In:= X\[ScriptCapitalD] = KernelMixtureDistribution[\!\(\* TagBox[ RowBox[{"EventData", "[", PanelBox["258", FrameMargins->Small], "]"}], InterpretTemplate[EventData[Automatic, Map[Developer`ToPackedArray, {{ 5, 6.75, 5, 5, 7.25, 4.25, 5.75, 6.25, 6.5, 4, 4.25, 4.75, 5.75, 2.75, 3.75, 5, 5.5, 6.5, 2.75, 3, 5.25, 5.25, 2.25, 3, 4, 4.5, 4.75, 5, 5.25, 5.25, 5.5, 5.5, 6, 3, 5.5, 2.25, 2.25, 2.25, 2.25, 2.5, 2.75, 3, 3.25, 3.25, 4, 4, 4, 1.25, 1.5, 2.5, 3, 3, 3.25, 3.75, 4.5, 4.5, 5, 5, 5.25, 5.25, 5.25, 5.25, 5.25, 2, 3.25, 3.5, 3.75, 4, 4, 4.25, 4.25, 4.25, 4.75, 4.75, 4.75, 5, 1.25, 1.75, 2, 2, 2.75, 3, 3, 3.5, 3.5, 4.25, 4.5, 1.25, 2.25, 2.25, 2.5, 2.75, 2.75, 3, 3.25, 3.5, 3.5, 4, 4, 4.25, 4.5, 4.5, 1.25, 1.75, 1.75, 2, 2.75, 3, 3, 3, 4, 4.25, 4.25, 1, 1.5, 1.5, 2, 2.25, 2.75, 3.5, 3.75, 3.75, 4, 1.25, 1.5, 1.5, 2, 2, 2, 2.25, 2.5, 2.5, 2.5, 3, 3.5, 3.5, 1, 1.5, 1.5, 1.5, 1.75, 2.25, 2.25, 2.5, 2.5, 2.5, 2.5, 2.75, 2.75, 2.75, 2.75, 3, 3, 3, 3.25, 3.25, 1, 1.5, 1.5, 1.5, 1.75, 1.75, 2, 2.25, 2.75, 3, 3, 3.25, 3.25, 3.25, 3.25, 3.25, 3.25, 0.5, 1.5, 1.5, 1.75, 2, 2.25, 2.25, 2.25, 2.5, 2.5, 3, 3, 3, 0.25, 0.25, 0.75, 0.75, 0.75, 1, 1, 1.25, 1.25, 1.5, 1.5, 1.5, 1.5, 2.25, 2.25, 2.5, 2.5, 2.75, 1, 1, 1, 1.25, 1.25, 1.75, 2, 2.25, 2.25, 2.5, 0.25, 0.25, 0.75, 1, 1.5, 1.5, 1.5, 2, 2, 2.25, 0.5, 0.75, 0.75, 0.75, 1, 1, 1, 1.25, 1.25, 1.5, 1.5, 1.75, 1.75, 1.75, 2, 0.75, 1, 1.25, 1.75, 1.75, 0.25, 0.25, 0.75, 1, 1.25, 1.5, 0.75, 0.75, 1, 1.25, 1.25, 1.25, 0.75, 0.25}, None, {{ DirectedInfinity[-1], 8}, { DirectedInfinity[-1], 7.75}, { DirectedInfinity[-1], 7.25}, { DirectedInfinity[-1], 7.25}, { DirectedInfinity[-1], 7.25}, { DirectedInfinity[-1], 7}, { DirectedInfinity[-1], 7}, { DirectedInfinity[-1], 7}, { DirectedInfinity[-1], 7}, { DirectedInfinity[-1], 6.75}, { DirectedInfinity[-1], 6.75}, { DirectedInfinity[-1], 6.75}, { DirectedInfinity[-1], 6.75}, { DirectedInfinity[-1], 6.5}, { DirectedInfinity[-1], 6.5}, { DirectedInfinity[-1], 6.5}, { DirectedInfinity[-1], 6.5}, { DirectedInfinity[-1], 6.5}, { DirectedInfinity[-1], 6.25}, { DirectedInfinity[-1], 6.25}, { DirectedInfinity[-1], 6.25}, { DirectedInfinity[-1], 6.25}, { DirectedInfinity[-1], 6}, { DirectedInfinity[-1], 6}, { DirectedInfinity[-1], 6}, { DirectedInfinity[-1], 6}, { DirectedInfinity[-1], 6}, { DirectedInfinity[-1], 6}, { DirectedInfinity[-1], 6}, { DirectedInfinity[-1], 6}, { DirectedInfinity[-1], 6}, { DirectedInfinity[-1], 6}, { DirectedInfinity[-1], 6}, { DirectedInfinity[-1], 5.75}, { DirectedInfinity[-1], 5.75}, { DirectedInfinity[-1], 5.5}, { DirectedInfinity[-1], 5.5}, { DirectedInfinity[-1], 5.5}, { DirectedInfinity[-1], 5.5}, { DirectedInfinity[-1], 5.5}, { DirectedInfinity[-1], 5.5}, { DirectedInfinity[-1], 5.5}, { DirectedInfinity[-1], 5.5}, { DirectedInfinity[-1], 5.5}, { DirectedInfinity[-1], 5.5}, { DirectedInfinity[-1], 5.5}, { DirectedInfinity[-1], 5.5}, { DirectedInfinity[-1], 5.25}, { DirectedInfinity[-1], 5.25}, { DirectedInfinity[-1], 5.25}, { DirectedInfinity[-1], 5.25}, { DirectedInfinity[-1], 5.25}, { DirectedInfinity[-1], 5.25}, { DirectedInfinity[-1], 5.25}, { DirectedInfinity[-1], 5.25}, { DirectedInfinity[-1], 5.25}, { DirectedInfinity[-1], 5.25}, { DirectedInfinity[-1], 5.25}, { DirectedInfinity[-1], 5.25}, { DirectedInfinity[-1], 5.25}, { DirectedInfinity[-1], 5.25}, { DirectedInfinity[-1], 5.25}, { DirectedInfinity[-1], 5.25}, { DirectedInfinity[-1], 5}, { DirectedInfinity[-1], 5}, { DirectedInfinity[-1], 5}, { DirectedInfinity[-1], 5}, { DirectedInfinity[-1], 5}, { DirectedInfinity[-1], 5}, { DirectedInfinity[-1], 5}, { DirectedInfinity[-1], 5}, { DirectedInfinity[-1], 5}, { DirectedInfinity[-1], 5}, { DirectedInfinity[-1], 5}, { DirectedInfinity[-1], 5}, { DirectedInfinity[-1], 5}, { DirectedInfinity[-1], 4.75}, { DirectedInfinity[-1], 4.75}, { DirectedInfinity[-1], 4.75}, { DirectedInfinity[-1], 4.75}, { DirectedInfinity[-1], 4.75}, { DirectedInfinity[-1], 4.75}, { DirectedInfinity[-1], 4.75}, { DirectedInfinity[-1], 4.75}, { DirectedInfinity[-1], 4.75}, { DirectedInfinity[-1], 4.75}, { DirectedInfinity[-1], 4.75}, { DirectedInfinity[-1], 4.5}, { DirectedInfinity[-1], 4.5}, { DirectedInfinity[-1], 4.5}, { DirectedInfinity[-1], 4.5}, { DirectedInfinity[-1], 4.5}, { DirectedInfinity[-1], 4.5}, { DirectedInfinity[-1], 4.5}, { DirectedInfinity[-1], 4.5}, { DirectedInfinity[-1], 4.5}, { DirectedInfinity[-1], 4.5}, { DirectedInfinity[-1], 4.5}, { DirectedInfinity[-1], 4.5}, { DirectedInfinity[-1], 4.5}, { DirectedInfinity[-1], 4.5}, { DirectedInfinity[-1], 4.5}, { DirectedInfinity[-1], 4.25}, { DirectedInfinity[-1], 4.25}, { DirectedInfinity[-1], 4.25}, { DirectedInfinity[-1], 4.25}, { DirectedInfinity[-1], 4.25}, { DirectedInfinity[-1], 4.25}, { DirectedInfinity[-1], 4.25}, { DirectedInfinity[-1], 4.25}, { DirectedInfinity[-1], 4.25}, { DirectedInfinity[-1], 4.25}, { DirectedInfinity[-1], 4.25}, { DirectedInfinity[-1], 4}, { DirectedInfinity[-1], 4}, { DirectedInfinity[-1], 4}, { DirectedInfinity[-1], 4}, { DirectedInfinity[-1], 4}, { DirectedInfinity[-1], 4}, { DirectedInfinity[-1], 4}, { DirectedInfinity[-1], 4}, { DirectedInfinity[-1], 4}, { DirectedInfinity[-1], 4}, { DirectedInfinity[-1], 3.75}, { DirectedInfinity[-1], 3.75}, { DirectedInfinity[-1], 3.75}, { DirectedInfinity[-1], 3.75}, { DirectedInfinity[-1], 3.75}, { DirectedInfinity[-1], 3.75}, { DirectedInfinity[-1], 3.75}, { DirectedInfinity[-1], 3.75}, { DirectedInfinity[-1], 3.75}, { DirectedInfinity[-1], 3.75}, { DirectedInfinity[-1], 3.75}, { DirectedInfinity[-1], 3.75}, { DirectedInfinity[-1], 3.75}, { DirectedInfinity[-1], 3.5}, { DirectedInfinity[-1], 3.5}, { DirectedInfinity[-1], 3.5}, { DirectedInfinity[-1], 3.5}, { DirectedInfinity[-1], 3.5}, { DirectedInfinity[-1], 3.5}, { DirectedInfinity[-1], 3.5}, { DirectedInfinity[-1], 3.5}, { DirectedInfinity[-1], 3.5}, { DirectedInfinity[-1], 3.5}, { DirectedInfinity[-1], 3.5}, { DirectedInfinity[-1], 3.5}, { DirectedInfinity[-1], 3.5}, { DirectedInfinity[-1], 3.5}, { DirectedInfinity[-1], 3.5}, { DirectedInfinity[-1], 3.5}, { DirectedInfinity[-1], 3.5}, { DirectedInfinity[-1], 3.5}, { DirectedInfinity[-1], 3.5}, { DirectedInfinity[-1], 3.5}, { DirectedInfinity[-1], 3.25}, { DirectedInfinity[-1], 3.25}, { DirectedInfinity[-1], 3.25}, { DirectedInfinity[-1], 3.25}, { DirectedInfinity[-1], 3.25}, { DirectedInfinity[-1], 3.25}, { DirectedInfinity[-1], 3.25}, { DirectedInfinity[-1], 3.25}, { DirectedInfinity[-1], 3.25}, { DirectedInfinity[-1], 3.25}, { DirectedInfinity[-1], 3.25}, { DirectedInfinity[-1], 3.25}, { DirectedInfinity[-1], 3.25}, { DirectedInfinity[-1], 3.25}, { DirectedInfinity[-1], 3.25}, { DirectedInfinity[-1], 3.25}, { DirectedInfinity[-1], 3.25}, { DirectedInfinity[-1], 3}, { DirectedInfinity[-1], 3}, { DirectedInfinity[-1], 3}, { DirectedInfinity[-1], 3}, { DirectedInfinity[-1], 3}, { DirectedInfinity[-1], 3}, { DirectedInfinity[-1], 3}, { DirectedInfinity[-1], 3}, { DirectedInfinity[-1], 3}, { DirectedInfinity[-1], 3}, { DirectedInfinity[-1], 3}, { DirectedInfinity[-1], 3}, { DirectedInfinity[-1], 3}, { DirectedInfinity[-1], 2.75}, { DirectedInfinity[-1], 2.75}, { DirectedInfinity[-1], 2.75}, { DirectedInfinity[-1], 2.75}, { DirectedInfinity[-1], 2.75}, { DirectedInfinity[-1], 2.75}, { DirectedInfinity[-1], 2.75}, { DirectedInfinity[-1], 2.75}, { DirectedInfinity[-1], 2.75}, { DirectedInfinity[-1], 2.75}, { DirectedInfinity[-1], 2.75}, { DirectedInfinity[-1], 2.75}, { DirectedInfinity[-1], 2.75}, { DirectedInfinity[-1], 2.75}, { DirectedInfinity[-1], 2.75}, { DirectedInfinity[-1], 2.75}, { DirectedInfinity[-1], 2.75}, { DirectedInfinity[-1], 2.75}, { DirectedInfinity[-1], 2.5}, { DirectedInfinity[-1], 2.5}, { DirectedInfinity[-1], 2.5}, { DirectedInfinity[-1], 2.5}, { DirectedInfinity[-1], 2.5}, { DirectedInfinity[-1], 2.5}, { DirectedInfinity[-1], 2.5}, { DirectedInfinity[-1], 2.5}, { DirectedInfinity[-1], 2.5}, { DirectedInfinity[-1], 2.5}, { DirectedInfinity[-1], 2.25}, { DirectedInfinity[-1], 2.25}, { DirectedInfinity[-1], 2.25}, { DirectedInfinity[-1], 2.25}, { DirectedInfinity[-1], 2.25}, { DirectedInfinity[-1], 2.25}, { DirectedInfinity[-1], 2.25}, { DirectedInfinity[-1], 2.25}, { DirectedInfinity[-1], 2.25}, { DirectedInfinity[-1], 2.25}, { DirectedInfinity[-1], 2}, { DirectedInfinity[-1], 2}, { DirectedInfinity[-1], 2}, { DirectedInfinity[-1], 2}, { DirectedInfinity[-1], 2}, { DirectedInfinity[-1], 2}, { DirectedInfinity[-1], 2}, { DirectedInfinity[-1], 2}, { DirectedInfinity[-1], 2}, { DirectedInfinity[-1], 2}, { DirectedInfinity[-1], 2}, { DirectedInfinity[-1], 2}, { DirectedInfinity[-1], 2}, { DirectedInfinity[-1], 2}, { DirectedInfinity[-1], 2}, { DirectedInfinity[-1], 1.75}, { DirectedInfinity[-1], 1.75}, { DirectedInfinity[-1], 1.75}, { DirectedInfinity[-1], 1.75}, { DirectedInfinity[-1], 1.75}, { DirectedInfinity[-1], 1.5}, { DirectedInfinity[-1], 1.5}, { DirectedInfinity[-1], 1.5}, { DirectedInfinity[-1], 1.5}, { DirectedInfinity[-1], 1.5}, { DirectedInfinity[-1], 1.5}, { DirectedInfinity[-1], 1.25}, { DirectedInfinity[-1], 1.25}, { DirectedInfinity[-1], 1.25}, { DirectedInfinity[-1], 1.25}, { DirectedInfinity[-1], 1.25}, { DirectedInfinity[-1], 1.25}, { DirectedInfinity[-1], 1}, { DirectedInfinity[-1], 0.75}}}]]& ], Editable->False, SelectWithContents->True, Selectable->True]\), .75]; Mean[\[ScriptCapitalD]]
 Out= #### The probability a person will survive more than six years without developing AIDS.

 In:= XProbability[t > 6, t \[Distributed] \[ScriptCapitalD]]
 Out= #### The expected induction time, given AIDS has not developed by six years.

 In:= XNExpectation[t \[Conditioned] t >= 6, t \[Distributed] \[ScriptCapitalD]]
 Out=  