(a) We seek k so that the function is normalized, as required by a true density. We
integrate this function, set it to 1.0,
k
⎡
⎣
ai
−∞
exp[(x − ai)/bi]dx +
∞
ai
exp[−(x − ai)/bi]dx
⎤
⎦ = 1,
which yields 2bik = 1 or k = 1/(2bi). Note that the normalization is independent
of ai, which corresponds to a shift along the axis and is hence indeed irrelevant
to normalization. The distribution is therefore written