(Stat 467 only) Let X₁,..., Xn be a random sample from standard uniform distribution. (a) Determine the cumulative distribution function (CDF) and the probability density function (PDF) of the first order statistic X (1) (the minimum of the sample). Make sure to properly account for the domains.

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6. (Stat 467 only) Let X₁,..., Xn be a random sample from standard
uniform distribution.
(a) Determine the cumulative distribution function (CDF) and the
probability density function (PDF) of the first order statistic X(1)
(the minimum of the sample). Make sure to properly account for
the domains.
(b) Determine the cumulative distribution function (CDF) and the
probability density function (PDF) of the largest order statistic
X(n) (the maximum of the sample). Make sure to properly account
for the domains.
(c) Graph the PDFs of X₁, X(1), and X(n) and write a short paragraph
explaining how the three distributions are different.
Transcribed Image Text:6. (Stat 467 only) Let X₁,..., Xn be a random sample from standard uniform distribution. (a) Determine the cumulative distribution function (CDF) and the probability density function (PDF) of the first order statistic X(1) (the minimum of the sample). Make sure to properly account for the domains. (b) Determine the cumulative distribution function (CDF) and the probability density function (PDF) of the largest order statistic X(n) (the maximum of the sample). Make sure to properly account for the domains. (c) Graph the PDFs of X₁, X(1), and X(n) and write a short paragraph explaining how the three distributions are different.
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