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Yet Another Proof of Sylvester's Determinant Identity
Jan Vrbik, Paul Vrbik
In 1857 Sylvester stated a result on determinants without proof that was recognized as important over the subsequent century. Thus it was a surprise to Akritas, Akritas and Malasch…
Playing Several Patterns Against One Another
Jan Vrbik, Paul Vrbik
We revisit the game in which each of several players chooses a pattern and then a coin is flipped repeatedly until one of these patterns is generated. In particular, we demonstrate…
Cumulants of products of Normally distributed random variables
Clarence Kalitsi, Jan Vrbik
To find moments of various estimators related to Autoregressive models of Statistics, one first needs the cumulants of products of two Normally distributed random variables. The pu…
Formula to evaluate a limit related to AR(k) model of Statistics
Yuhao Liu, Jan Vrbik
Computing moments of various parameter estimators related to an autoregressive model of Statistics, one needs to evaluate several expressions of the type mentioned in the title of…