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Suppose that X is a single observation from a Binomial(n, p) distribution where n is known...

Suppose that X is a single observation from a Binomial(n, p) distribution where n is known and 0 < p < 1 is unknown. Consider three estimators of p: pˆ = X /n “sample proportion” pˆA = (X + 2)/ (n + 4) “plus four estimator” pˆB = (X + (√n/4))/( n + √ n ). “constant MSE estimator” (a) Find the bias functions for all three estimators. (b) Find the variance functions of all three estimators. (c) Find the MSE functions of all three estimators. (d) Create plots of the bias, variance, and MSE of all three estimators when n = 4. Note: I encourage you to use software of your choice. If you plot by hand, make sure that you have well defined scales and that you can see where the functions cross one another. That is, your plots should be more than just rough sketches. (e) Repeat the previous part for n = 40. (f) Repeat the previous part for n = 400. (g) Using your plots as evidence, discuss the relative merits of the three estimators. What are some advantages/disadvantages of each?

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orchestra answered 2 years ago
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