(a) Let X1, , Xn be a random sample from a Poisson distribution with parameter Icirc raquo Derive a (1 Icirc plusmn ) 100 large sample confidence interval for Icirc raquo (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, Phylogenetic dating with confidence intervals using mean path lengths) Assume that the data (given in centimeters) follow a Poisson distribution with parameter Icirc raquo Obtain a 95 confidence interval for l and interpret 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

Question: (a) Let X1, . . ., Xn be a random sample from a Poisson distribution with parameter Î». Derive a (1 Î±) 100% large sample

(a) Let X1, . . ., Xn be a random sample from a Poisson with parameter Î». Derive a (1 €“ Î±) 100% large sample confidence interval for Î».
(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 with parameter Î».

Obtain a 95% confidence interval for l and interpret.

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

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