7) Consider the random variable Y~ N(10, 25). Suppose you are interested in the following alternative...

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7) Consider the random variable Y~ N(10, 25). Suppose you are interested in the following alternative estimator for the mean of Y: N 1 n - 1 μ = Yi i=1 a) Prove that this estimator is biased by (1) calculating by hand the bias of this estimator and (2) use R to simulate 10,000 random draws of sample size n=5 of Y, plotting them in a histogram, and adding a red vertical line at the true mean value (μ = 10). Provide both the calculated bias and the histogram here. (Hint: Use the abline() function to add the red vertical line.) b) Show that the estimator is still consistent by (1) showing by hand that the estimator converges to the true mean value µ, and (2) in R run the same simulation as in (a) but increase the sample size to n=1000, plot the 10,000 estimates in a histogram, and again add a red vertical line at the true mean. 7) Consider the random variable Y~ N(10, 25). Suppose you are interested in the following alternative estimator for the mean of Y: N 1 n - 1 μ = Yi i=1 a) Prove that this estimator is biased by (1) calculating by hand the bias of this estimator and (2) use R to simulate 10,000 random draws of sample size n=5 of Y, plotting them in a histogram, and adding a red vertical line at the true mean value (μ = 10). Provide both the calculated bias and the histogram here. (Hint: Use the abline() function to add the red vertical line.) b) Show that the estimator is still consistent by (1) showing by hand that the estimator converges to the true mean value µ, and (2) in R run the same simulation as in (a) but increase the sample size to n=1000, plot the 10,000 estimates in a histogram, and again add a red vertical line at the true mean.

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a To calculate the bias of the estimator ... View the full answer