5. Incorrect. The answer is true not false.

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%