Trying to figure out how to find the values of A and B? How would I start? I am working on my Statics homework, and I came across a problem that I didn't even know where to begin. I want to know how to do part (a) after that I can figure out the other parts. The problem is > A random variable $X$ takes values between 0 and $\infty$ with a cumulative distribution function $F_X(x) = A + Be^{-x}$ for $0 \le x \le \infty$ > > (a) Find the values of A and B and sketch the cumulative distribution function.

Since the random variable does not take values before $0$, $$ F(0) = 0 $$ Since the random variable can take on any nonnegative value, we must have: $$ \lim_{x \to \infty} F(x) = 1 $$ Using these facts we see that:

> $$\begin{align}F(0) &= 0 & \lim_{x \to \infty} F(x) &= 1 \\\ A + Be^0 &= 0 & \lim_{x \to \infty} \left[ A + Be^{-x} \right] &= 1 \\\ A + B &= 0 & A &= 1 \\\ 1 + B &= 0 \\\ B &= -1\end{align}$$