STAT231 Study Guide - Midterm Guide: Confidence Interval, Likelihood Function, Prediction Interval
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We adopt the model iy poisson i(cid:79) (cid:32) P y (cid:32) y (cid:32) (cid:79)(cid:79) (cid:16) y y e y (cid:32) Sd y (cid:32) (cid:79: (3 marks) show that the maximum likelihood estimate of (cid:79) is. Context 1 in a survey of a rural area in ontario five years ago, the average number of song sparrows was 2. 43 per hectare. To see if the population size has changed, the area was divided into 10,000 one hectare plots and a sample of 30 plots was selected at random. In each selected plot, the number of song sparrows y was determined . 1 (cid:32) i (cid:166)(cid:32) y c exp{ 30 } (cid:79) (cid:79) i (cid:166) c ln( ) (cid:79) (cid:32) (cid:14) (cid:16) ln( ) 30 y i. The log likelihood function is ( ) (cid:79) l (cid:16) (cid:79) and (cid:32) y i (cid:79) Setting the derivative to 0 and solving we get dl (cid:79) d (cid:79)
