Question: Let Z1, Z2, . . . be a sequence of random variables, and suppose that for n = 2, 3, . . . , the

Let Z1, Z2, . . . be a sequence of random variables, and suppose that for n = 2, 3, . . . , the of Yn is as follows:
Pr(Yn = 1/n) = 1− 1/n2 and Pr(Yn = 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?

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