# Probability Density Function with continuous random variables

Let $X$ have density $$f_X(x) = \begin{cases} \sqrt{3(x+2)}/6 & -2 \leq x \leq 1 \\ 0 & \text{otherwise}. \end{cases}$$ Find the probability that $X$ is positive.

Would this just be the integral from $0$ to $1$?

• Yes- that would be the answer! – voldemort Apr 18 '14 at 4:59
• @user139388 I do not know how to use HTML. Thanks for the edit. – Brent Apr 24 '14 at 0:55

To find the probability that $X$ is positive implies that $\int^1_0 f_X(x)$ is what we are looking for.Evaluate that integral to get the probability that X is positive.
I think your answer will be $\displaystyle 1 - \frac{2 \sqrt{2}}{3\sqrt{2}} \approx 0.45567$