P(Xn=ki)=P(Xn≤ki+0.1)−P(Xn≤ki−0.1)→→P(X≤ki+0.1)−P(X≤ki−0.1)=P(X=ki)
since the unique integer value ki belongs to the interval (ki−0.1,ki+0.1]. The convergence takes place since CDF of X is continuous at the points
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manpreet![Tuteehub forum best answer]()
Best Answer
3 years ago
There is a n">question in a syllabus called "Mathematische statistiek":
"If every XnXn and XX possess a discrete distribution supported on a finite set of integers, show that XnXnconverges in distribution to XX iff P(Xn=x)→P(X=x)P(Xn=x)→P(X=x) for every xx."
This is what I tried: First assume the convergence holds. Let k1<k2<...<knk1n be all the integers XXcan reach. For i∈N−{1}i∈N−{1} we have