# Please explain uniform distribution to me [duplicate]

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I am confused about Uniform Distribution why does $$P(v < 2b1)$$

equal 2b1 ?

## marked as duplicate by Did, Amzoti, user127.0.0.1, Hans Lundmark, LutzLApr 22 '14 at 22:09

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• The game theory question deals with the wider theory and why we do certain calculations, this deal with individual calculations and how to do them which calculations to do vs how to do them – S F Apr 22 '14 at 21:21

## 1 Answer

I guess $v$ is a random variable of uniform distribution on the interval $[0,1]$. Then, if $0\le b_1\le 1/2$, we indeed have

$P(v<2b_1)=$ length of $[0,2b_1)$ which is $2b_1$.

• thanks but How do you get the length ? – S F Apr 22 '14 at 21:22
• We have $P(v\in S)=\lambda(S)$ for any measurable $S$ where $\lambda$ denotes the Lebesgue measure on the line, i.e. the length. The full event has probability $P(v\in [0,1])=1$ and the empty event has $P(v\in empty)=0$. – Berci Apr 22 '14 at 21:27