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Let $X$ be a Random Variable with pdf $f_x(x)=1/2$ for $-1<x<1$.

$Y=I_{[X>0.75]}=\begin{cases} 1 & \quad \text{if } x>0.75\\ 0 & \quad \text{if } x \leq 0.75\\ \end{cases}$

Find the pmf of the random variable Y

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    $\begingroup$ $Y$ is discrete, so it has no pdf, it has a pmf. $\endgroup$ – Ian Oct 28 '15 at 0:16
  • $\begingroup$ And obviously $\mathsf P(Y{=}1) = \mathsf P(\boxed{\,?\,}), \mathsf P(Y{=}0) = \mathsf P(\boxed{\,?\,})$ $\endgroup$ – Graham Kemp Oct 28 '15 at 0:30
  • $\begingroup$ I have sloved it, thank you for your hints. $\endgroup$ – Lysla Ri Oct 28 '15 at 1:31

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