dratini1570

if X and Y are uniform random (0,1) and H=(X+2)Y, then the distribution for H looks like the piecewise graph y={0.4: 0<x<2, 1.2-.4x, 2<x<3}, which i estimated using simulation

upon further consideration (using math not simulation), the function for H is {0<x<2: ln(3)-ln(2), 2<x<3: ln(3)-ln(x)} (piecewise) the graph of H: desmos.com/calculator/jf384j0mrt the probability graph that P(ln(H)>z): desmos.com/calculator/io40jln2nx