1. **Problem:** Sketch a graph of the uniform probability distribution of $X$, where $X$ is the time in minutes from when the alarm is set to when it goes off, uniformly distributed from $-2$ to $2$ minutes. 2. **Formula and explanation:** For a uniform distribution on $[a,b]$, the probability density function (pdf) is $$f(x) = \frac{1}{b - a}$$ for $x$ in $[a,b]$, and zero otherwise. 3. **Apply to this problem:** Here, $a = -2$ and $b = 2$, so $$f(x) = \frac{1}{2 - (-2)} = \frac{1}{4}$$ for $-2 \leq x \leq 2$. 4. **Graph description:** The graph is a rectangle from $x = -2$ to $x = 2$ with height $\frac{1}{4}$. 5. **Final answer:** The uniform probability distribution of $X$ is $$f(x) = \begin{cases} \frac{1}{4}, & -2 \leq x \leq 2 \\ 0, & \text{otherwise} \end{cases}$$ This completes the sketch and description of the uniform distribution for $X$.