Consider a Bernoulli model, iid Y,..., Yn Bernoulli (0), 0 ...

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Consider a Bernoulli model, iid Y₁,..., Yn Bernoulli (0), 0 <0 <1, and the following data observed from that model: y (0,1,0,1,0) For this question you may use without proof that = y, and approximately, as well as 0-0 √0(1-0)/n 0-0 √√(1-6)/n ~G(0, 1) ~G(0, 1) approximately. (a) (1 point) Compute an approximate 95% confidence interval for based on the second of the two Gaussian approximations above, i.e. using equation (4.6) from page 153 of the course notes. (b) (3 points) Show that the roots (in 0) of the quadratic equation 0² (1+2/2/n)-0(20+2/2/n) + ² = 0 define an approximate (1-a)100% confidence interval for 0, where %a/2 satisfies P(Z <%a/2) = x/2 for Z G(0, 1). (c) (2 points) Compute an approximate 95% confidence interval for based on (b). (d) (2 points) Give a formula for a relative likelihood interval for that is also a 95% confidence interval for 0. Your formula can be in terms of an equation that must be solved numerically. Compute the interval for these data. (e) (2 points) Which interval is preferable for inference? List at least two reasons supporting your position. Consider a Bernoulli model, iid Y₁,..., Yn Bernoulli (0), 0 <0 <1, and the following data observed from that model: y (0,1,0,1,0) For this question you may use without proof that = y, and approximately, as well as 0-0 √0(1-0)/n 0-0 √√(1-6)/n ~G(0, 1) ~G(0, 1) approximately. (a) (1 point) Compute an approximate 95% confidence interval for based on the second of the two Gaussian approximations above, i.e. using equation (4.6) from page 153 of the course notes. (b) (3 points) Show that the roots (in 0) of the quadratic equation 0² (1+2/2/n)-0(20+2/2/n) + ² = 0 define an approximate (1-a)100% confidence interval for 0, where %a/2 satisfies P(Z <%a/2) = x/2 for Z G(0, 1). (c) (2 points) Compute an approximate 95% confidence interval for based on (b). (d) (2 points) Give a formula for a relative likelihood interval for that is also a 95% confidence interval for 0. Your formula can be in terms of an equation that must be solved numerically. Compute the interval for these data. (e) (2 points) Which interval is preferable for inference? List at least two reasons supporting your position.