Align: one line centered and the next right-justified

Question

Consider the following code:

\documentclass{amsart}
\usepackage{amsthm, amssymb, amsfonts}

\begin{align*}
F_{X^2}(x) = P(X^2 \leq x) = P(X \leq \sqrt{x}) = F_{X}(\sqrt{x}) = 
    \sqrt{x}
\\
F_{Y^2}(y) = P(Y^2 \leq y) = P(-\sqrt{y} \leq Y \leq \sqrt{y}) =
    F_{Y(\sqrt{y}) - F_{Y}(-\sqrt{y}) = 
\\
\frac{\sqrt{y}- (-1)}{2} - \frac{- \sqrt{y}-(-1)}{2} = \sqrt{y}
\end{align*}

\end{document}

Note I am making two statements, the first of which takes one line, and the second of which takes up two lines. As written, all three lines are right-justified. It would seem that it would make more sense to the reader if the first line were centered, and the third line were right-justified, so that it is clear that it is a continuation of line two. Does anyone have a tip for how to achieve this? Should I make the first line its own block, in other words, use $$$$ for the first line, and align for the second line?

Any other suggestions as to how to make my meaning visually clear are welcome.

Answer 1

I propose two possibilities (I guessed the definition of \p)

\documentclass[reqno, 11pt]{amsart}
\usepackage{mathtools}
\DeclareMathOperator\p{P}

\begin{document}
First attempt:
\begin{align*}
F_{X^2}(x) &= \p(X^2 \leq x) = \p(X \leq \sqrt{x}) = F_{X}(\sqrt{x}) = \sqrt{x}
\\
F_{Y^2}(y) &=
  \!\begin{multlined}[t]
  \p(Y^2 \leq y) = \p(-\sqrt{y} \leq Y \leq \sqrt{y}) =
    F_{Y}(\sqrt{y}) - F_{Y}(-\sqrt{y}) = \\
  \frac{\sqrt{y}- (-1)}{2} - \frac{- \sqrt{y}-(-1)}{2} = \sqrt{y}
  \end{multlined}
\end{align*}

Second attempt:
\begin{align*}
F_{X^2}(x) &= \p(X^2 \leq x) = \p(X \leq \sqrt{x}) = F_{X}(\sqrt{x}) = \sqrt{x} \\[2ex]
F_{Y^2}(y) &= \p(Y^2 \leq y) = \p(-\sqrt{y} \leq Y \leq \sqrt{y}) \\
           &= F_{Y}(\sqrt{y}) - F_{Y}(-\sqrt{y}) =
  \frac{\sqrt{y}- (-1)}{2} - \frac{- \sqrt{y}-(-1)}{2} = \sqrt{y}
\end{align*}

\end{document}

I would prefer the second one, actually, that makes the development clearer, in my opinion.

Answer 2

Here's an example that, as an alternative, stacks the rows with different alignments, rather than using the align environment. The space between the rows is controlled, as well.

\documentclass{amsart}
\usepackage{amsthm, amssymb, amsfonts}
\usepackage{stackengine}
\stackMath
\begin{document}
\def\stackalignment{l}\stackanchor[3ex]{%
F_{X^2}(x) = P(X^2 \leq x) = P(X \leq \sqrt{x}) = F_{X}(\sqrt{x}) = 
    \sqrt{x}
}{%
\def\stackalignment{r}\stackunder[1.5ex]{%
F_{Y^2}(y) = P(Y^2 \leq y) = P(-\sqrt{y} \leq Y \leq \sqrt{y}) =%
    F_Y(\sqrt{y}) - F_{Y}(-\sqrt{y}) %
}{\displaystyle%
= \frac{\sqrt{y}- (-1)}{2} - \frac{- \sqrt{y}-(-1)}{2} = \sqrt{y}%
}%
}
\end{document}