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Please answer all parts of the question, with all work shown Suppose there are 300 cards...

Please answer all parts of the question, with all work shown

Suppose there are 300 cards in a box numbered 1 through 300. Therefore, the number of each card has one, two, or three digits. A card is drawn at random from the box. Suppose that the number on the card has X digits of which Y are 0. Suppose we would like to know whether X and Y are correlated, negatively correlated, or uncorrelated. Determine Cov(X,Y)Cov(X,Y) and ρ(X,Y)ρ(X,Y), hence settling the question.

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