Let U ∼ Unif(0,1) and X ∼ Expo(1) , independently. The probability density function (pdf) of U × X is:
a) f(u × x) = e⁻ˣ
b) f(u × x) = e-(u+x)
c) f(u × x) = e⁻ˣ for 0 < u × x < 1 and f(u × x) = 0 otherwise
d) f(u × x) = e-(u+x) for 0 < u × x < 1 and f(u × x) = 0 otherwise