calc2 problem

jamster114 · November 19th 2006, 07:13 PM

How can I solve this?

**ThePerfectHacker** · November 19th 2006, 07:28 PM

First,
$p(x)\geq 0$ .

Next we need to find,
$\int_{-\infty}^{\infty} p(x)dx$
Subdivide the interval as,
$\int_{-\infty}^0p(x)dx+\int_0^{\infty}p(x)dx$
Since the integral is continous accept at possibly one point we can chose to ignore that fact.
Now,
$\int_{-\infty}^0 p(x)dx=0$ because $p(x)=0$ for $x<0$ .

And,
$\int_0^{\infty} p(x)dx=\int_0^{\infty} \lambda e^{-\lambda x}dx$

The anti-derivative is,
$e^{-\lambda x} | ^{\infty}_0 =1$
So it is indeed a probability density function.

Thread: calc2 problem

LinkBack

Thread Tools

Display

calc2 problem

Similar Math Help Forum Discussions

Calc2: Not sure where to begin...

[SOLVED] Calc2...Finding the volume

solving diffyQ for calc2

Calc2 - Dx with ln

Integration: calc2