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Find a sequence of uniformly bounded discrete independent random variables <math>\{X_n\}</math> such that the variance of their sum does not tend to <math>\infty</math> as <math>n | |||
variables <math>\{X_n\}</math> such that the variance of their sum does not tend to <math>\infty</math> as <math>n | |||
\rightarrow \infty</math>, and such that their sum is not asymptotically normally distributed. | \rightarrow \infty</math>, and such that their sum is not asymptotically normally distributed. | ||
Latest revision as of 23:14, 14 June 2024
Find a sequence of uniformly bounded discrete independent random variables [math]\{X_n\}[/math] such that the variance of their sum does not tend to [math]\infty[/math] as [math]n \rightarrow \infty[/math], and such that their sum is not asymptotically normally distributed.