2 Let U1, U2, be a sequence of independent random variables each of which is uniformly distributed over the interval 0, 1 Consider a sequence of random variables X1, X2, such that Xn max U1, , Un , n 1, 2, Determine whether or not the sequence Xn converges i) almost surely, ii) in rth mean, iii) in probability, iv) in distribution, and identify the limit, if any

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2 Let U1, U2,       be a sequence of independent random variables each of which is uniformly distributed over the interval  0, 1   Consider a sequence of random variables X1, X2,       such that Xn   max U1,       , Un , n   1, 2,       Determine whether or not the sequence Xn converges i) almost surely, ii) in rth mean, iii) in probability, iv) in distribution, and identify the limit, if any

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Question: 2 Let U1, U2, . . . be a sequence of independent random variables each of which is uniformly distributed over the interval [0, 1].

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