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I have two uniformly dirstributed random variables $$r_1 = \mathcal{U}(0,1)$$ and $$r_2 = \mathcal{U}(0,1)$$. I am looking for the probability distribution of $$max\{r_1, r_2\}$$. Is there any known distribution?

Xafer
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  • Please search the site. See https://math.stackexchange.com/q/495958/321264, https://math.stackexchange.com/q/215801/321264 for example. – StubbornAtom Jun 11 '20 at 14:39

1 Answers1

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Hint

You can't compute it if you don't know the joint ditribution of $(r_1,r_2)$ or if $(r_1,r_2)$ are not independent. If you know the joint distribution or if they are independent, remark that

$$\mathbb P(\max\{r_1,r_2\}\leq x)=\mathbb P(r_1\leq x,r_2\leq x).$$

kola
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