Contents of 31-2
Experimental Probability in Elementary School P34. Lane Andrew
Concepts in probability can be more readily understood if students are first exposed to probability via experiment. Performing probability experiments encourages students to develop understandings of probability grounded in real events, as opposed to merely computing answers based on formulae.
The Colour of Money P37. Mike Fletcher
We consider how probability theory can be used to increase one’s chances of winning in the new television game show The Colour of Money.
An Inside Look at the Two Envelopes Paradox P39. Ruma Falk¹ and Raymond S. Nickerson
When two sealed envelopes contain money, one twice as much as the other, a player should be indifferent between them. But when one envelope is opened, one’s decision should vary as a function of the observed value and one’s subjective probabilities.
Explanatory Power and Statistical Significance P42. Joseph G. Eisenhauer
Very little explanatory power is required in order for regressions to exhibit statistical significance. This article discusses some of the causes and implications.
The Correlation between Two Random Variables in a Coin-Tossing Experiment P47. Jyoti P. Shiwalkar and M.N. Deshpande
We find the correlation of two jointly distributed random variables connected with a coin tossing experiment. The marginal distributions are binomial and negative binomial.
Statistics Online Computational Resource for Education P49. Ivo D. Dinov and Nicolas Christou
The Statistics Online Computational Resource (http://www.SOCR.ucla.edu) provides one of the largest collections of free Internet-based resources for probability and statistics education. SOCR develops, validates and disseminates two core types of materials – instructional resources and computational libraries.
How to Show That Sample Size Matters P52. Marcin Kozak
This article suggests how to explain a problem of small sample size when considering correlation between two Normal variables. Two techniques are shown: one based on graphs and the other on simulation.
Variance of a Few Observations P55. Anwar H. Joarder
This article demonstrates that the variance of three or four observations can be expressed in terms of the range and the first order differences of the observations. A more general result, which holds for any number of observations, is also stated.
Knowing Your Limitations P59. Colin Foster
This article reflects on whether probability statements can usefully be made about one-off exceptional events.