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Calculating the covariance of two discrete random variables

  • #1

Homework Statement


If the random variables T and U have the same joint probability function at the following five pairs of outcomes: (0, 0), (0, 2), (-1, 0), (1, 1), and (-1, 2). What is the covariance of T and U?

Homework Equations


σxy = E(XY) - μx⋅μy

The Attempt at a Solution


My issue with this problem is interpreting what is meant by each of the points having the same joint probability function. The only way I am able to proceed is by considering that the joint probability function (whatever that may be for the two variables) evaluated at each of the five outcomes returns the same value. In other words, each of the five outcomes listed above have an equal probability of occurring. I am able to find the covariance if this is the case.

Is this interpretation of the problem statement correct? If not, what is the proper interpretation? I have no difficulty with the mathematical operations associated with this problem, I'm just not sure if I'm understanding the problem statement.

Any help is appreciated.
 
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Answers and Replies

  • #2
Ray Vickson
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Homework Statement


If the random variables T and U have the same joint probability function at the following five pairs of outcomes: (0, 0), (0, 2), (-1, 0), (1, 1), and (-1, 2). What is the covariance of T and U?

Homework Equations


σxy = E(XY) - μx⋅μy

The Attempt at a Solution


My issue with this problem is interpreting what is meant by each of the points having the same joint probability function. The only way I am able to proceed is by considering that the joint probability function (whatever that may be for the two variables) evaluated at each of the five outcomes returns the same value. In other words, each of the five outcomes listed above have an equal probability of occurring. I am able to find the covariance if this is the case.

Is this interpretation of the problem statement correct? If not, what is the proper interpretation? I have no difficulty with the mathematical operations associated with this problem, I'm just not sure if I'm understanding the problem statement.

Any help is appreciated.
I think your "equi-probable" assumption is the only reasonable interpretation of this poorly-worded problem. If I were doing it I would assume each of the five points has probability 1/5, and I would also add the statement that I was assuming those five points are exhaustive (i.e., that all other points have zero probabilities --- not stated in the problem as you wrote it).
 
  • #3
Thank you for chiming in; it's good to know I'm not the only one who thought the wording was a bit murky.
 

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