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Maximum of four uniforms in a band

EasyProbabilityRandom Variables~3m

Let X1,X2,X3,X4∼Uniform(0,4)X_1, X_2, X_3, X_4 \sim \text{Uniform}(0, 4) be independent. What is the probability that max⁡iXi\max_i X_i lies in the interval (2,3](2, 3]?

Show hints (2)+
  1. P(max⁡≤x)=(x/4)4\mathbb{P}(\max\le x)=(x/4)^4 since all four must be ≤x\le x.
  2. Subtract: (3/4)4−(2/4)4(3/4)^4-(2/4)^4.

Answer

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0.2539 (± 0.001)

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