Find the indicated probability.
-$$\mathrm { f } ( \mathrm { x } ) = \mathrm { e } ^ { - \mathrm { x } ; } ; [ 0 , \infty ) , \mathrm { P } ( \mathrm { x } \geq 7 )$$
A) $0.9991$
B) 0
C) $0.0009$
D) The function $\mathrm { f } ( \mathrm { x } )$ is not a probability density function.

Question

Quizplus · Accepted Answer

To find the probability that $x \geq 7$, we need to integrate the probability density function from 7 to infinity:
$$\begin{aligned} \mathrm{P}(x \geq 7) &= \int_{7}^{\infty} e^{-x} dx \ &= \left[-e^{-x}\right]_{7}^{\infty} \ &= \lim_{t \to \infty}-e^{-t} - (-e^{-7}) \ &= e^{-7} \ &= 0.00091188... \end{aligned}$$
Therefore, the best choice is C: 0.0009.

Find the Indicated Probability f(x)=e−x;;[0,∞),P(x≥7)\mathrm { f } ( \mathrm { x } ) = \mathrm { e } ^ { - \mathrm { x } ; } ; [ 0 , \infty ) , \mathrm { P } ( \mathrm { x } \geq 7 )f(x)=e−x;;[0,∞),P(x≥7)

Find the Indicated Probability $\mathrm { f } ( \mathrm { x } ) = \mathrm { e } ^ { - \mathrm { x } ; } ; [ 0 , \infty ) , \mathrm { P } ( \mathrm { x } \geq 7 )$