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I have the following distribution:

$$P(Z \leq z ) = \begin{cases} z/20 & 0 < x <10 \\ 1/2 + z/200 & 10 \leq z < 110 \\ 1 & z > 110 \end{cases} $$

How can I write this as a mix of two uniform distributions? For reference, the cdf of U(a,b) is (x - a)/(b - a), and the pdf is 1/(b - a).

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    $\begingroup$ Should $z$ be $x$? And this function can't be a cumulative distribution function since it's not increasing. Perhaps you mean for it to be a density function? $\endgroup$ – Greg Martin Sep 18 at 5:42
  • $\begingroup$ fixed @GregMartin $\endgroup$ – user702736 Sep 18 at 9:26
  • $\begingroup$ I think maybe it's still wrong. I'm trying to find the equilibrium distribution of a random variable that is $10$ with probability $0.1$ and $110$ with probability $0.1$. Can you help me? That is what the distribution function is supposed to be $\endgroup$ – user702736 Sep 18 at 9:37
  • $\begingroup$ The equilibrium distribution is $X$ is $F_{e}(x) = \frac{1}{E(X)} \int_{0}^x P(X > x)$. $\endgroup$ – user702736 Sep 18 at 9:37
  • $\begingroup$ If you mean the underlying variable is 10 with probability 0.9, I think you have the right formula. The probabilities 0.1 and 0.1 don't add up to 1, so that cannot be what you wanted. $\endgroup$ – David K Sep 18 at 10:55

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