Question

Compute the mean, standard deviation, and covariance matrix. Also consider appropraite for of equation to use given the number of data avialable as appropriate (see below)

1.2 Given the following data 0.5 0.7 0.9 03 0.6 0.5 0.1 0.3 0.7 0.0 06 0.3 0.2 0.4 0.4 0.3 0.3 -0.1 0.4 0.5 0.2 0.7 0.3 -0.4 0.9 0.1 0.0 1.3 0.6 0. compute the mean, standard deviation and covariance matrix for these data, quoting all num- bers to two signfiicant figures. Carefully consider the appropriate form of equation to use given the number of data available aus appropriate

Answer 1

I will be using excel to solve this. I am atatching screenshot for everything

Mean of x:

Mean of y:

Mean of z:

Standard Deviation of x

Standard Deviation of y:

Standard Deviation of z:

Upto 2 Significant figures:

Formula for Covariance is given as:

So we will find Covariance between (X,X), (Y,Y), (Z,Z), (X,Y), (Y,Z), (X,Z)

Using the excel,

In our case N = 10 for all X, Y and Z

So,

Cov(X,X) = $\sum$ [(X - mean(X)) * (X - mean(X))] / N

Cov(X,X) = 2.789 / 10 = 0.2789 = 0.28

Similraly,

Cov(Y,Y) = 0.324 / 10 = 0.0324 = 0.03

Cov(Z,Z) = 1.444 / 10 = 0.1444 = 0.14

Cov(X,Y) = 0.1287 / 10 = 0.01287 = 0.013

Cov(Y,Z) = 0.0553 / 10 = 0.00553 = 0.0055

Cov(X,Z) = 0.5363 / 10 = 0.0536 = 0.054