Let {X,}E, be i.i.d. uniform random variables in [0, 0), for some 0 > 0. Denote by Mn = max=1,2,..,n X4. Prove that M, converges in probability to 0. Compute the cumulative distribution function ofn...

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Let {X,}E, be i.i.d. uniform random variables in [0, 0), for some 0 > 0. Denote by Mn = max=1,2,..,n X4.<br>Prove that M, converges in probability to 0.<br>Compute the cumulative distribution function ofn (1– Mn/0) and prove that n (1 – Mn/0) converges in distribution<br>to an exponential random variable with parameter 1.<br>

Extracted text: Let {X,}E, be i.i.d. uniform random variables in [0, 0), for some 0 > 0. Denote by Mn = max=1,2,..,n X4. Prove that M, converges in probability to 0. Compute the cumulative distribution function ofn (1– Mn/0) and prove that n (1 – Mn/0) converges in distribution to an exponential random variable with parameter 1.

Jun 11, 2022

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Let {X,}E, be i.i.d. uniform random variables in [0, 0), for some 0 > 0. Denote by Mn = max=1,2,..,n X4. Prove that M, converges in probability to 0. Compute the cumulative distribution function ofn...

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