# probability of a number in a range where the upper and lower bound is randomly draw from a distribution

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 where x is a random number in [0,1].

• What is $x$ here? – d.k.o. Nov 4 at 14:43
• Question: how are the values chosen? Are $a,b$ chosen such that they are "meaningful"? Or is it possible that $b<a$? – InterstellarProbe Nov 4 at 14:43
• 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 $b$. – Leo163 Nov 4 at 14:44
• @Leo163 "If x is uniformly chosen from $\mathbb{R}$" doesn't make sense. – d.k.o. Nov 4 at 14:47
• As you can see from the comments, your question is not clear. Please edit for clarity. – lulu Nov 4 at 14:49