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Let Z₁, Z2,... be a sequence of random variables, and suppose that for n = 2, 3,..., the distribution of Zn is as follows: P(Zn = 1/n) = 1-1/n², P(Zn = n) = 1/n².
(a) Does there exist a constant c to which the sequence converges in probability? (b) Does there exist a constant c to which the sequence converges in quadratic mean?
Sagot :
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