Question

The time until a chemical reaction is complete (in milliseconds) has the density function f(x) = e^-x/100/100 for x ≥ 0.

a. Determine the mean and variance of x.

b. P(X>100).

Answer 1

$a:\\X~Exp\left( 0.01 \right) \Rightarrow EX=\frac{1}{0.01}=100,DX=\frac{1}{0.01^2}=10000\\b:\\P\left( X>100 \right) =\int_{100}^{+\infty}{\frac{e^{-x/100}}{100}dx}=-e^{-x/100}|_{100}^{+\infty}=e^{-1}$