I try to solve a probability.

a and b are i.i.d. draw from a distribution, for example, 1) uniform distribution and 2) Poisson distribution in [0,1].

How to solve $Prob(a<x<b)$ where x is a random number in [0,1].

  • $\begingroup$ What is $x$ here? $\endgroup$ – d.k.o. Nov 4 at 14:43
  • $\begingroup$ Question: how are the values chosen? Are $a,b$ chosen such that they are "meaningful"? Or is it possible that $b<a$? $\endgroup$ – InterstellarProbe Nov 4 at 14:43
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    $\begingroup$ How do you choose $x$? If $x$ is uniformly chosen from $\mathbb{R}$, the probability is going to be $0$ no matter how you pick $a$ and $b$. $\endgroup$ – Leo163 Nov 4 at 14:44
  • $\begingroup$ @Leo163 "If x is uniformly chosen from $\mathbb{R}$" doesn't make sense. $\endgroup$ – d.k.o. Nov 4 at 14:47
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    $\begingroup$ As you can see from the comments, your question is not clear. Please edit for clarity. $\endgroup$ – lulu Nov 4 at 14:49

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