1. Suppose {Xn, n 1} is a sequence of random variables with X~ Binomial(n, pn) such that np.1 >0 as n . Show that as n ,P(X= k) e-11 k k! for k= 0, 1, 2,...2. A Poisson GLM is used to model the annual number of polititians switching political parties in the USA during 1802-1876.(a) Explain why a Poisson GLM is approporiate to model the data.(b) Eleven explanatory variables are used in the linear predictor, one of which is whether or not the year is a non-election year, denoted as non-elect (non-elect=1 if non-election year, 0 if election year). The estimated coefficient of non-elect is 1.051. Interpret the meaning of this coefficient.(c) The estimated standard error for the estimated coefficient of non-elect is 0.320. Is non-elect statistically significant?(d) Obtain a 90% confidence interval of the coefficient of non-elect.

1. Suppose {X, n 2 1} is a sequence of random variables with X, ~ Binomial(n, p.) such that np, -> > > 0 as n + co. Show that as n + 00. P(Xn = k) - for k = 0, 1, 2. . .. k! 2. A Poisson GLM is used to model the annual number of polititians switching political parties in the USA during 1802-1876. (a) Explain why a Poisson GLM is approporiate to model the data. (b) Eleven explanatory variables are used in the linear predictor, one of which is whether or not the year is a non-election year, denoted as non-elect (non-elect=1 if non-election year, () if election year). The estimated coefficient of non-elect is 1.051. Interpret the meaning of this coefficient. (c) The estimated standard error for the estimated coefficient of non-elect is 0.320. Is non-elect statistically significant? (d) Obtain a 90% confidence interval of the coefficient of non-elect