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CDF of a maximum of uniforms

EasyRandom VariablesStatistics~3m

X1,…,X4X_1,\dots,X_4 are independent uniform [0,1][0,1]. The CDF of max⁡iXi\max_i X_i is F(x)=x4F(x)=x^4. Evaluate FF at x=0.5x = 0.5. (to 4 decimals)

Show hints (2)+
  1. max ≤ x means every X_i ≤ x.
  2. F(x) = xⁿ for n iid uniforms.

Answer

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0.0625

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Asked at: Optiver, Akuna Capital

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