Davy Crockett, a U.S. congressman during the 1830s, published A Narrative of the Life of David Crockett, Written by Himself. In a Chance (Spring 1999) article, researchers determined that x, the number of times (per 1,000 words) that the word though appears in the Life narrative, has a mean of .25. Assume that x has an approximate Poisson distribution.
a. Find the variance of x.
b. Calculate the interval μ ± 2σ. What proportion of the time will x fall into this interval?
c. In 1836, Davy Crockett died at the Alamo defending Texans from an attack by the Mexican general Santa Anna. The following year, the narrative Colonel Crockett’s Exploits and Adventures in Texas was published. Some historians have doubts whether Crockett was the actual author of this narrative. In the Texas narrative, “though” appears twice in the first 1,000 words. Use this information and your answer to part b to make an inference about whether Crockett actually wrote the Texas narrative. (Assume that the Life narrative was really written by Davy Crockett.)