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pr 1 X and Y are two random variables. A scatter diagram for a 15 different samples of both random variables is illustrated below a. Suggest a convenient value for the covariance of X, Y 2 pt 2 t. Is X, Y independent? Why? If they are dependent and you know that X-10, what you could expect about Y? GOOD LUCK

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Answer #1

Answer:

a).

when x increases, y decreases. The relation is negative. The covariance is a negative value.

Possible value may be around -2

Note:

approximate calculation for covariance.

Assume correlation is about -0.9 and by range rule, sy=range/4=1.25 and sx=range/4=1.75

Covariance = r*sx*sy = -0.9*1.25*1.75 = -1.968

b). X and Y are not independent because clearly when x increases y decreases.

When X=10 we expect Y value is around 1.

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