I am working on a problem that is finding the CDF of a random variable X from a density function that has an absolute value. My question shares some similarity to this one where I imagine to solve it, you need to use some sort of splitting of the integration.
The problem: Find the CDF for the random variable from:
f(x) = $|x|\over10$, on -2$\le$x$\le$4
0, otherwise
What I have done so far:
Fx(x) = $\int_{-\infty}^{-2}$f(x) d(x) = 0
Fx(x) = $\int_{-2}^4$ f(x) d(x) = 1
The CDF is something along the lines of:
Fx(x) = $1\over10$$\int_{a}^0$|x|d(x) + $1\over10$$\int_{0}^{a}$|x|d(x)
Not sure if I am on the right track here
Best Answer
$F(y) = \int_{-\infty}^y f(x) \ dx$
if $y< 0$
$F(y) = \int_{-2}^y \frac {-x}{10} \ dx$
if $y\ge 0$
$F(y) = \int_{-2}^0 \frac {-x}{10} \ dx + \int_0^y \frac {x}{10} \ dx$
Giving you a piece-wise function.