Introduction to Probability

CHAPTER 5COVARIANCE AND CORRELATION

George U. Yule (Morham, Scotland 1871 – Cambridge, England 1951)

George Udny Yule was born on 18 February 1871, in Morham, Scotland, and died on 26 June 1951, at the age of 80, in Cambridge, England. At the age of 16, he entered University College London to study Engineering. Then, in 1893, he returned to University College to work as a demonstrator for Karl Pearson, whose interest in the field of Statistics he followed. During 1897–1899, he wrote many important papers on correlation and regression, while three decades later he published a key paper dealing with spurious correlation. In 1912, he moved to Cambridge University and stayed there till the end of his career. In 1911, he published an influential textbook Introduction to the Theory of Statistics, which was highly successful and went through fourteen editions. Through his work on the theory of evolution in 1925, he introduced a stochastic process which is now called Yule process, and the resulting distribution is also called Yule distribution.

5.1 INTRODUCTION

In Chapter 3, we discussed the concept of independence between two or more random variables. When two variables are independent, then the value that one of them takes on does not have any effect on the values that the other variable may take on. Although this statement seems to deserve no further elaboration, when two variables ...