Do Propositions 1 and 2 cover the situation of Exercise 10? Exercise 10 Consider i.i.d. r.v.s X

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Do Propositions 1 and 2 cover the situation of Exercise 10?


Exercise 10

Consider i.i.d. r.v.’s X1,X2, ... assuming a finite number of values x1 2 m. 

(a)Describe the behavior of the r.v.’simage

andimage

heuristically.

(b) Provide a rigorous explanation. How “fast” do the distributions ofimage approach their limits (if any)?

(c) Describe the cases where we cannot expect a similar behavior ofimage

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