Page 353, 5.4.4.* Let X and Yn be 1-dimensional random variables such that Xn and Yn are independent for each n and their mgfs exist. Show that if Xn →X in distribution and Yn → Yin distribution, where X and Y are 1-dimensional random variables, then Xn - Yn →X-Y, in distribution.

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Page 353 5.4.4
Page 353, 5.4.4.* Let X and Yn be 1-dimensional
random variables such that X and Yn are
n
independent for each n and their mgfs exist.
Show that if Xn →X in distribution and Yn → Y in
distribution, where X and Y are 1-dimensional
random variables, then Xn - Yn →X-Y, in
distribution.
Transcribed Image Text:Page 353, 5.4.4.* Let X and Yn be 1-dimensional random variables such that X and Yn are n independent for each n and their mgfs exist. Show that if Xn →X in distribution and Yn → Y in distribution, where X and Y are 1-dimensional random variables, then Xn - Yn →X-Y, in distribution.
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