Let X and Y be two random variables, denoting the age and weight (in kg), respectively....

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Let X and Y be two random variables, denoting the age and weight (in kg), respectively. Consider a random sample of size n = 20 from these two variables: X = {28, 50, 61, 72, 80, 51, 20, 35, 28, 97, 37, 64, 46, 67, 34, 21, 21, 59, 46, 46) Y = {62, 87, 88, 109, 95, 104, 58, 82, 70, 102, 67, 104, 83, 89, 69, 68, 65, 103, 78, 102) (a) Find the mean and median of X. (b) Find the variance of X. (Use population variance, i.e normalize by total number of observations) (c) Find the 2-dimensional mean u d) Find the covariance matrix between these two variables. (Do not use the built-in function) (e) Find the eigenvalues and eigenvectors of the covariance matrix. (Do not use the built-in function) (f) What is the probability of observing an age of 75 or higher? (g) What is the correlation between age and weight? (Do not use the built-in function) (h) Draw the scatter plot of the variable Y versus the variable X. Let X and Y be two random variables, denoting the age and weight (in kg), respectively. Consider a random sample of size n = 20 from these two variables: X = {28, 50, 61, 72, 80, 51, 20, 35, 28, 97, 37, 64, 46, 67, 34, 21, 21, 59, 46, 46) Y = {62, 87, 88, 109, 95, 104, 58, 82, 70, 102, 67, 104, 83, 89, 69, 68, 65, 103, 78, 102) (a) Find the mean and median of X. (b) Find the variance of X. (Use population variance, i.e normalize by total number of observations) (c) Find the 2-dimensional mean u d) Find the covariance matrix between these two variables. (Do not use the built-in function) (e) Find the eigenvalues and eigenvectors of the covariance matrix. (Do not use the built-in function) (f) What is the probability of observing an age of 75 or higher? (g) What is the correlation between age and weight? (Do not use the built-in function) (h) Draw the scatter plot of the variable Y versus the variable X.

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