# calc2 problem

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• Nov 19th 2006, 08:13 PM
jamster114
calc2 problem
How can I solve this?

http://i15.tinypic.com/2ymzyop.jpg
• Nov 19th 2006, 08:28 PM
ThePerfectHacker
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.
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