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)
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) = [(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
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