=λ. Consider a sequence N₁ = X₁+... Xn, where the Xi's are iid, Poisson distributed, and E[X1] ✓ What can you say about the quantity n-¹N when n is large? In other words, does lim→∞ n¯¹Nn exist? If so, precisely describe in what stochastic sense it exists and characterize the limit.

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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=λ.
Consider a sequence N₁ = X₁+... Xn, where the Xi's are iid, Poisson distributed, and E[X1]
✓ What can you say about the quantity n-¹N when n is large? In other words, does lim→∞ n¯¹Nn
exist? If so, precisely describe in what stochastic sense it exists and characterize the limit.
Transcribed Image Text:=λ. Consider a sequence N₁ = X₁+... Xn, where the Xi's are iid, Poisson distributed, and E[X1] ✓ What can you say about the quantity n-¹N when n is large? In other words, does lim→∞ n¯¹Nn exist? If so, precisely describe in what stochastic sense it exists and characterize the limit.
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