Question: Let X 1 , X 2 , X 3 , be a sequence of random variable such that where > 0 is a

Let X1, X2, X3, ⋯ be a sequence of random variable such thatXn Poisson (n), for n = 1,2,3,...,

where λ > 0 is a constant. Define a new sequence Yn asYn 1 Xn n for n = 1, 2, 3,....

Show that Yn converges in mean square to λ, i.e., Yn m.s.→ λ.

Xn Poisson (n), for n = 1,2,3,...,

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