Q.1 Let x be the number of kittens born, and Y be the number of kittens survived for a certain breed of kittens. Suppose the following table describes joint probability distribution of x and Y :
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Q.1 Let X be the number of kittens born, and Y be the number of kittens survived for a certain breed of kittens. Suppose the following table describes joint probability distribution of X and Y :
X 1 2 0.03 0.02 K 0.03 0.05 0.04
Y 3 4 5
0 0.31 0.21 0.21
3 0.01 0.02 0.03
(i) Obtain K so that it is the joint probability mass function: (ii) Find cumulative distribution function Fx.y(x, y); (iii) Find conditional probability density functions i.e. f(Y|X)(v|x) = P{(Y=y|X=x)}and f(X|Y)(x|y)=P{(X=x|Y=y)}; (iii) Find Conditional expectations and variances, i.e. E[Y|X= xl,E[X|Y = y],V[Y|X=x] andV[X|Y=y]; (iv) Are random variables X and Y independent?
