I would like to understand what does this problem mean by "defining" a random variable. I know that $W$ represents the maximum of the order statistics $X_1$, $X_2$, $X_3$, and that $Z$ represents their minimum.
1.But what does "defining" these variables mean in this context?
2.Does it mean calculating their pdf and their distribution function?
3.If so, how? What would be the definition of the desity range function?
I'd appreciate a lot any help or guidance on solving it, thanks!
Let $X_1$, $X_2$, $X_3$ be independent random variables with an uniform distribution $\mathcal{U}(0,1)$.
- Define $W=\max(X_1,X_2,X_3)$ and $Z=\min(X_1,X_2,X_3)$.
- Find the density range function $R=W-Z$.
