Contracts for two construction jobs are randomly assigned to one or more of three firms. A, B, and C. The joint distribution of X, the number of contracts awarded to firm A, and Y, the number of contracts awarded to firm B, is given by the entries in the following table: Y X 0 1 2 0 1/9 2/9 1/9 1 2/9 2/9 0 2 1/9 0 0 a) Calculate P(X<2, Y<2) b) Find the marginal probability distribution of the random variables X and Y c) Determine whether the random variables X and Y are independent d) Find the conditional density functions p(x|y=1) and p(x|y=0) e) Calculate the expected value of XY f) Find the covariance of X and Y g) Find the correlation coefficent of X and Y
Contracts for two construction jobs are randomly assigned to one or more of three firms. A, B, and C. The joint distribution of X, the number of contracts awarded to firm A, and Y, the number of contracts awarded to firm B, is given by the entries in the following table: Y X 0 1 2 0 1/9 2/9 1/9 1 2/9 2/9 0 2 1/9 0 0 a) Calculate P(X<2, Y<2) b) Find the marginal probability distribution of the random variables X and Y c) Determine whether the random variables X and Y are independent d) Find the conditional density functions p(x|y=1) and p(x|y=0) e) Calculate the expected value of XY f) Find the covariance of X and Y g) Find the correlation coefficent of X and Y
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 5SE: Answer the following questions. 5. What is the term for the arrangement that selects r objects from...
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Contracts for two construction jobs are randomly assigned to one or more of three firms. A, B, and C. The joint distribution of X, the number of contracts awarded to firm A, and Y, the number of contracts awarded to firm B, is given by the entries in the following table:
| Y | |||
| X | 0 | 1 | 2 |
| 0 | 1/9 | 2/9 | 1/9 |
| 1 | 2/9 | 2/9 | 0 |
| 2 | 1/9 | 0 | 0 |
a) Calculate P(X<2, Y<2)
b) Find the marginal probability distribution of the random variables X and Y
c) Determine whether the random variables X and Y are independent
d) Find the conditional density
e) Calculate the
f) Find the
g) Find the
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