Question

The density of a bivariate normal distribution with mean equal to (0,0) and correlation matrix equal to ? = [1.0 0.5; 0.5 1.0] is f(x,y) = 1/(??3) exp[-2(x^2 + y^2 - xy)/3]. Write R code that will create objects x and y that are each equal to the sequence {-3.00, -2.95, ..., 2.95, 3.00}. Then create a matrix z and populate it with the values of f(x,y) for each combination of x and y values. A nested for loop can be used to do this. Once this has been completed create a contour plot of the data. The lines on the plot should be red.

          The density of a bivariate normal distribution with mean equal to (0,0) and correlation matrix equal to
? = [1.0 0.5; 0.5 1.0]
is
f(x,y) = 1/(??3) exp[-2(x^2 + y^2 - xy)/3].
Write R code that will create objects x and y that are each equal to the sequence {-3.00, -2.95, ..., 2.95, 3.00}. Then create a matrix z and populate it with the values of f(x,y) for each combination of x and y values. A nested for loop can be used to do this. Once this has been completed create a contour plot of the data. The lines on the plot should be red.

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The density of a bivariate normal distribution with mean equal to (0,0) and correlation matrix equal to
? = [1.0 0.5; 0.5 1.0]
is
f(x,y) = 1/(??3) exp[-2(x^2 + y^2 - xy)/3].
Write R code that will create objects x and y that are each equal to the sequence -3.00, -2.95, ..., 2.95, 3.00. Then create a matrix z and populate it with the values of f(x,y) for each combination of x and y values. A nested for loop can be used to do this. Once this has been completed create a contour plot of the data. The lines on the plot should be red.

Added by Jessica R.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Evelyn Cunningham

Step 1

First, we need to create the objects x and y that are each equal to the sequence {-3.00, -2.95, 2.95, 3.00}. We can use the `seq()` function in R to create these sequences. ```R x <- seq(-3, 3, by = 0.05) y <- seq(-3, 3, by = 0.05) ``` Show more…

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The density of a bivariate normal distribution with mean equal to (0,0) and correlation matrix equal to ρ = [1.0 0.5; 0.5 1.0] is f(x,y) = 1/(π√3) exp[-2(x^2 + y^2 - xy)/3]. Write R code that will create objects x and y that are each equal to the sequence {-3.00, -2.95, ..., 2.95, 3.00}. Then create a matrix z and populate it with the values of f(x,y) for each combination of x and y values. A nested for loop can be used to do this. Once this has been completed create a contour plot of the data. The lines on the plot should be red.

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