In this note a new proof of the divergence of the harmonic series is given based on the expected life of a parallel system with independent exponentially distributed component lifetimes.

In this note, we discuss a coin tossing experiment with a new stopping rule. The two random variables involved in the experiment have some interesting properties.

A truncated version of the Cauchy distribution is introduced. Unlike the Cauchy distribution, this possesses finite moments of all orders and could therefore be a better model for certain practical situations. One such situation in finance is discussed. Explicit expressions for the moments of the truncated distribution are also derived.

A simple, direct condition is formulated for determining the mode(s) of a probability mass function. This condition is then applied to the Poisson and hypergeometric mass functions.

Quantiles for finite mixtures of normal distributions are computed. The difference between a linear combination of independent normal random variables and a linear combination of independent normal densities is emphasized. (Contains 3 tables and 1 figure.)

This note considers functions of two variables which are continuous on a possibly unbounded closed region in [vertical bar]R[squared], and the functions of one variable obtained by integrating out the other variable over this region. The question of continuity of these functions is investigated, as are connections with joint density and marginal…

This note introduces an interesting random walk on a straight path with cards of random numbers. The method of recurrent relations is used to obtain the convergent probability of the random walk with different initial positions.

This short note introduces an interesting random walk on a circular path with cards of numbers. By using high school probability theory, it is proved that under some assumptions on the number of cards, the probability that a walker will return to a fixed position will tend to one as the length of the circular path tends to infinity.