(a) Let X1, . . ., Xn be a random sample from a Poisson distribution with parameter λ. Derive a (1 €“ α) 100% large sample confidence interval for λ.
(b) To date nodes in a phylogenetic tree, the mean path length (MPL) is used in estimating the relative age of a node. The following data represent the MPL for 39 nodes (source: TomBritton, Bengt Oxelman, Annika Vinnersten, and Kare Bremer, €œPhylogenetic dating with confidence intervals using mean path-lengths€). Assume that the data (given in centimeters) follow a Poisson distribution with parameter λ.

Obtain a 95% confidence interval for l and interpret.

Transcribed Image Text:

65.2 47.0 38.2 13.5 18.0 25.6 16.3 14.0 23.2 18.8 7.5 13.3 1.0 54.9 22.0 50.1 326 26.0 3.0 9.0 7.2 4.7 4.5 4. 45.8 37.0 8.5 30.5 29.3 13.8 7.7 5.5 24.1 12.5 22.3 19.0 9.5 4.7 3.0