Weird Density function
Could someone help me with this, please? Thanks!
Given the following probability density function
p(x) = (3/4)*(1-x^2) for |x|<1
p(x) = 0 otherwise
I need to find the probability that the random variable X falls between 0 and 1/2 (i.e. 0<X<1/2)
Integrating from -1 to 1 the density function, I find its area equals -(1/2).
Am I doing sometihng wrong?
Yes you are. Look at the integral again.
Originally Posted by paolopiace
I really don't know how I went wrong on that trivial integral...
Always take advantage of the even functions.
is even, since (You may confirm this easily.)
This leads easy computations and prevent to get mistaken.