Let X and Y have the joint pm f given by a Find the marginal

Let X and Y have the joint p.m. f. given by (a) Find the marginal p.m.f.?s and the means and the variances. (b) Sketch the support of X and Y. (e) Are X and Y independent? Justify your answer. (d) Find the covariance and the correlation coefficient of X and Y, (e) Find the best-fitting line and draw it on your figure from (d).

Solution

Mean of x = sum of px = 3.45

Var x = 13.31-3.45%2 =1.4075

Mean of Y = 1.97

var of Y = 4.55-1.97^2=0.6691

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P(X=1,y=3) = 0.02 not a multiple of P(x=1) and P(Y=2)

Not independent.

1	2	3	4	5
0.02	0.03	0.06	0.15	0.07	0.32
0.02	0.02	0.08	0.12	0.06	0.33
0.05	0.05	0.06	0.13	0.05	0.35
0.09	0.13	0.2	0.4	0.18	1