If-the-density-function-of-X-equals-f-x-c-e-2x-0-lt-x-lt-0-x-lt-0-find-c-What-is-P-X-gt-2-

Question Number 6604 by WAI LIN last updated on 05/Jul/16

I f t h e d e n s i t y f u n c t i o n o f X e q u a l s

f (x) = {\begin{cases} c e^{- 2 x}, 0 < x < \infty \\ 0, x < 0 \end{cases}

f i n d c . W h a t i s P {X > 2} ?

Commented by prakash jain last updated on 05/Jul/16

\int_{0}^{\infty} {c e}^{- 2} d x \neq 1

So f (x) is not a valid probability density

function .

Commented by WAI LIN last updated on 05/Jul/16

N o w I h a v e a n s w e r .

Commented by WAI LIN last updated on 05/Jul/16

S o r r y! B e f r o e m y q u e s t i o n i s w r o n g .

Answered by WAI LIN last updated on 05/Jul/16

\int_{0}^{\infty} f (x) d x = 1

\int_{0}^{\infty} c e^{- 2 x} d x = 1

- \frac{c}{2} {[e^{- 2}]}_{0}^{\infty} = 1

\frac{c}{2} = 1

∴ c = 2

N e x t, P (X > 2) = \int_{2}^{\infty} 2 e^{- 2 x} d x = - {[e^{- 2 x}]}_{2}^{\infty} = e^{- 4}

Facebook Tweet Pin