Recall the joint distribution of bananas and apples given in HW#7. Suppose that the bananas all weigh 120 g and the apples all weigh 85 g. Then we can define W=120 X +85Y to represent the total weight of bananas and apples purchased by the customer. Note that ?X=3.05 , ?Y=1.5 , ? X 2 =2.8475 , ?Y 2=0.91 , and Cov( X ,Y )=?1.825 .

a) (2) Determine E(120 X+85Y ) .

b) (4) Determine V(120 X+85Y ) .

c) (2) Determine the correlation, Corr (X ,Y ) .

d) (2) What does the correlation suggest about strength and direction of the relationship between these two variables?

e) (2) Determine P(X = 3 | Y = 2).

f) (2) Determine the conditional distribution of X given that Y=2.

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