# Math Help - Detemine A (random variable)

1. ## Detemine A (random variable)

A random variable X has pdf
$
f(x)=\begin{cases}
A(10 - x) \; , \qquad 5 \le x < 10 \\
\end{cases}$

i) Determine A
ii) Find $P(2.5 \le X \le 7.5)$

2. Originally Posted by Stats
A random variable X has pdf
$
f(x)=\begin{cases}
A(10 - x) \; , \qquad 5 \le x < 10 \\
\end{cases}$

i) Determine A
ii) Find $P(2.5 \le X \le 7.5)$
As with most of the questions you have asked, apply the basic definitions and formulas:

i) Use the fact that $\int_{- \infty}^{+ \infty} f(x) \, dx = 1$.
ii) Calculate $\int_{2.5}^{7.5} f(x) \, dx = 1$.

Note that the rule for f(x) is different over different intervals.