Infinite divisibility of Euclidean random variables and vectors has been a core theme in the theory of probability for at least sixty years. The question asked is when can a random variable be decomposed into small independent components. Precisely, a random variable (vector) $X$ is called infinitely divisible if for…

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Bulletin Editor Anirban DasGupta writes: The problem asked was to settle the possibility of consistent estimation with incomplete data in three examples, and to provide a concrete one when consistent estimation is possible. Intuitively, in case (a), you can only infer about $|\mu |$, but not the sign of $\mu…

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In this issue, we look at the consequences of having only incomplete data. For example, suppose a random variable $X$ has a normal distribution with mean $\mu$ and variance ${\sigma }^2$, and both parameters need to be estimated. With usual data, which we call complete data, namely iid copies…

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Bulletin Editor Anirban DasGupta writes: Well done to Yixin Wang of Columbia University, who sent correct answers to all three parts (although fuller answers are encouraged). The problem asked was to characterize the set of recurrence points of three $d$-dimensional random walks with step distributions $F$: (a) $d = 1,…

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The Student Puzzle printed in the April/May IMS Bulletin is clearly proving difficult to crack. So, to encourage more entries, the deadline has now been extended until June 18, 2015. Good luck…!…

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