Question: (a) Zn a in probability as n , (b) Zn a in probability as n , (c) if Un = n(1 Zn)

(a) Zn → a in probability as n → ∞,

(b) √Zn →√a in probability as n →∞,

(c) if Un = n(1 − Zn) and a = 1, then P(Un ≤ x) →

(

1 − e−x if x > 0, 0 otherwise, so that Un converges in distribution to the exponential distribution as n → ∞.

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