Question

Three independent samples of size ni = 100. n2-150, and n3 = 75 are se- lected respectively from Poisson(01), Poisson(02), and Poisson(93). The sample means respectively are 1.3, 1.65, 1.57. Use the asymptotic properties of MLE and Bonferroni inequality to compute 95% simultaneous confidence intervals for (91-82) and (02-83).

Answer 1

As it is a poison distribution therefore the parameter estimated  $\Theta _{1}$,$\Theta _{2}$,$\Theta 3$ is equal the mean of their poison distribution

therefore,estimate of  $\Theta _{1}$ is

$\Theta _{2}$ is

1.65

$\Theta 3$ is

1.57

From Z score table value of Z at
95
percent is $\pm 1.96$

so, confidence interval of $\Theta _{1}$ minus $\Theta _{2}$ can be obtain by

loD iSD - (-0 3S)(t o 30364) (-0.35 0.30 36 Чノー035t 0.30364 6536 Jo4636

loD iSD - (-0 3S)(t o 30364) (-0.35 0.30 36 Чノー035t 0.30364 6536 Jo4636

Similarly the confidence interval of $\Theta _{2}$ minus $\Theta 3$ is obtained by

5 0.08- (± 0.350 25)