Question

In: Statistics and Probability

The joint probability distribution of variables X and Y is shown in the table below. ...............................................................................X..........................................................................

The joint probability distribution of variables X and Y is shown in the table below.

...............................................................................X.......................................................................

Y

1

2

3

1

0.30

0.18

0.12

2

0.15

0.09

0.06

3

0.05

0.03

0.02

  1. Calculate E(XY)

  1. Determine the marginal probability distributions of X and Y.

           

  1. Calculate E(X) and E(Y)

           

  1. Calculate V(X) and V(Y)

           

  1. Are X and Y independent? Explain.

           

  1. Find P(Y = 2| X = 1)

  1. Calculate COV(X,Y). Did you expect this answer? Why?

  1. Find the probability distribution of the random variable X + Y.     

i.   Calculate E(X + Y) directly by using the probability distribution of X + Y.

              

  1. Calculate V(X + Y) directly by using the probability distribution of X + Y, and verify that V(X + Y) = V(X) + V(Y). Did you expect this result? Why?

Solutions

Expert Solution

orchestra answered 1 year ago
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