Question: Let Xn be a sequence of random variables that converges in distribution to a random variable X. Let Yn be a sequence of random variables

Let Xn be a sequence of random variables that converges in to a random variable X. Let Yn be a sequence of random variables with the property that for any finite number c,

Show that for any finite number c,

(This is the type of result used in the discussion of the power properties of the tests described in Section 10.3.2.)

lim P(y, > c) = 1. lim P(Xn + Yn > c) = 1.

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