Sample from a poisson distribution with parameter

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Reference no: EM13965424

1. (a) Let X1,..., Xn be a random sample from a Poisson distribution with parameter λ. Derive a (1 - α)100% large sample con?dence 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: Tom Britton, Bengt Oxelman, Annika Vinnersten, and Kåre Bremer, "Phylogenetic dating with con?dence intervals using mean path-lengths"). Assume that the data (given in centimeters) follow a Poisson distribution with parameter λ.

65.2	47.0	38.2	13.5	18.0	25.6	16.3	14.0	23.2	18.8
7.5	13.3	11.0	54.9	22.0	50.1	32.6	26.0	13.0	9.0
7.2	4.7	4.5	41.1	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

Obtain a 95% con?dence interval for λ and interpret.

Reference no: EM13965424

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