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Suppose that a particle is fired from the origin in the $(x,y)$-plane in a straight line in a direction at random angle $\Phi$ to the $x$-axis, and let $Y$ be the $y$-coordinate of the place where the particle hits the line ${x=1}$.

Can $\Phi$ bee seen as a random variable here? I want to think so but I'm not sure.

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    What hinders you from identifying $\Phi$ as a random variable?2012-11-05
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    Sure. If nothing is specified, you are probably intended to assume that $\Phi$ is uniformly distributed in the interval $[0,2\pi)$. It may be useful to deal separately with positive and negative $Y$.2012-11-05
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    Yes in the next sentence after the last sentence it says that $\Phi$ is uniform in the interval $(-\frac\pi2,\frac\pi2)$.2012-11-05
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    That is more sensible than my choice, though it makes no difference.2012-11-05

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