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Let X1, X2, - -- be the digits in the binary expansion of a uniform [0,1] variable U 2 23:1 Xn2_". (a) Describe the joint distribution of (X1, ....

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QQ截图20180904230057.png

1. Let X1, X2, - -- be the digits in the binary expansion of a uniform [0,1] variable U 2
23:1 Xn2_”. (a) Describe the joint distribution of (X1, . . . ,Xn) on {0, 1}“. (b) Modify the construction of U from X1,X2,... to create V 2 22:1 chn for suitable constants on so that V has the distribution on the Cantor set described
in Durrett’s Example 1.2.4.

Top Answer

1) a)  P ( ( X ​ 1 ​ ​ , . . . , X ​ n ​ ​ ) = x ​ n ​ ​ ) = ​ 2 ​ n ​ ​ ​ ​ 1 ​ ​ ∀ x... View the full answer

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