Answer
a. $P(0\leq X \leq 1) \approx 0.632$
b. $P(1 \leq X \leq 2) \approx 0.233$
c. $P(X \leq 2) \approx 0.865$
Work Step by Step
We are given $f(x)=e^{-x}; [0;\infty)$
a. $P(0\leq X \leq 1)$
$ =\int^{1}_{0}e^{-x}dx$
$=-e^{-x}|^{1}_{0}$
$\approx 0.632$
b. $P(1 \leq X \leq 2)$
$ =\int^{5}_{1}e^{-x}dx$
$=-e^{-x}|^{2}_{1}$
$\approx 0.233$
c. $P(X \leq 2)$
$ =\int^{2}_{\infty}e^{-x}dx$
$=-e^{-x}|^{2}_{\infty}$
$\approx 0.865$
