The length of life X for fuses of a certain type is modeled by the exponential
distribution, with
f (x) = e⁻ˣ ; 0 < x < [infinity] (1)
and f (x) = 0; otherwise.
Let continuous r.v.X1,X2 be independent and identically distributed with exp (1) density as given in (1).

a) If two such fuses have independent lengths of life X1 and X2, find their joint probability density function.