We saw at the start of the quarter some motivations for using the sample mean. Consider...

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We saw at the start of the quarter some motivations for using the sample mean. Consider the following method for choosing a 'representative value' for the middle of a distribution. Consider the squared difference of a data point from this representative value (which we will call m). This squared difference is for observation i. If we have n observations, i.e. ¿ = 1,..., n, then this average is the mean square error, i.e. 1 n n Σ(y: - μ)2 i=1 (a) Consider choosing µ to minimize mean square error. To do this, take first derivatives of this and set to zero (i.e. obtain the first order condition). This will solve very easily for µ as a function of the data points. (b) Comment on your result. We saw at the start of the quarter some motivations for using the sample mean. Consider the following method for choosing a 'representative value' for the middle of a distribution. Consider the squared difference of a data point from this representative value (which we will call m). This squared difference is for observation i. If we have n observations, i.e. ¿ = 1,..., n, then this average is the mean square error, i.e. 1 n n Σ(y: - μ)2 i=1 (a) Consider choosing µ to minimize mean square error. To do this, take first derivatives of this and set to zero (i.e. obtain the first order condition). This will solve very easily for µ as a function of the data points. (b) Comment on your result.

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a To choose to minimize the mean square error you can take the first derivative of the mean squar... View the full answer