**5. Correct.** **The answer is
true.**

a) We have to derive the
cummulative probability function so as to obtain the density function (it is an
application of the *fundamental theorem of
calculus*):

b) By definition of the complement of a probability *P(x ≤ 2 ) = 1 - P(x >2 )*:

*P(x>2) = 1 - (1-e ^{-4})
= e^{-4 }≈^{ }1.83%*

c) *P(2 ≤
x ≤ 4) = P( x ≤ 4) - P( x ≤ 2)* = F(4) - F(2) *≈* 1.79%