Suppose that two variables, X and Y, represent the number of movies watched by a

Question

Suppose that two variables, X and Y, represent the number of movies watched by a randomly
selected student per week and the number of courses taken by the student during thissemester.
Assume that variables (X, Y) have the joint distribution characterized by thefollowing equalities:
P (X = 0, Y = 2) = P (X = 1, Y = 2) = P (X = 2, Y = 2) = P (X = 0, Y = 4) = P (X = 2, Y = 4),and all those probabilities are 20% each.

Find:
a) What is the expected number E(X) of movies watched by students?
b) What is the expected number E(Y) of courses taken by students?
c) Find the covariance between X and Y, Cov(X, Y) =

Explanation / Answer

E(x)= 0*.2 +1*.2 +2*.2+ 0*.2 +2*.2 =1 E(y)= 2*.2 +2*.2+2*.2+ 4*.2+4*.2= 2.8 Covariance equals [(0-1)(2-2.8) + (1-1)(2-2.8) + (2-1)(2-2.8) +(0-1)(4-2.8) +(2-1)(4-2.8)]/4 I'll let you do the math on the last one.

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