4 Consider a bivariate random variable X Y that takes the va

4. Consider a bivariate random variable (X, Y) that takes the value (0, 0) with probability ¼, the value (1, 1 ) with probability 1/2, and the value (2, 0) with probability lit (a) Find the covariance of X and Y. (b) Are X and Y independent? Explain. 5. In how many ways can a club with eight members select a President, Vice President, Secretary, and a Treasurer from its membership?

Solution

(4)(a) cov =0*0.25*0+1*1*0.5+2*0*0.25 = 0.5

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(b) Since P(X=0, Y=0)=0.25 is not equal to P(X=0)*P(Y=0)=0.25*0.5, X and Y are not independent.

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(5) 8C4 = (8*7*6*5)/(1*2*3*4) =70

	X=0	X=1	X=2
Y=0	0.25	0	0.25
Y=1	0	0.5	0