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In this paper we have extended the notion of statistical limit point as introduced by Fridy[8] to I-statistical limit point of sequences of real numbers and studied some basic properties of the set of all I-statistical limit points and I-statistical cluster points of real sequences.

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We introduce the notions of strongly $\lambda$-statistically pre-Cauchy and strongly Vall´ee-Poussin pre-Cauchy sequences in probabilistic metric spaces endowed with strong topology. And we show that these two new notions are equivalent. Strongly $\lambda$-statistically convergent sequences are strongly $\lambda$-statistically pre-Cauchy sequences, and we give an example to show that there is a sequence in a probabilistic metric space which is strongly $\lambda$-statistically pre-Cauchy but not strongly $\lambda$-statistically convergent.