Problem 4. Fill in the in the previous probler X Y a 0.1 b 0.1 0.1 d. 0.05 e 0.15

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**Problem 4:**

Fill in the blanks to make a probability model whose "marginal probabilities" are those in the previous problem, if this is possible. If not, explain why not. 

**Table:**

|   | X   | Y   | Z   |
|---|-----|-----|-----|
| a | 0.1 |     |     |
| b |     |     |     |
| c | 0   |     | 0.01|
| d | 0.05|     |     |
| e |     | 0   |     |
| f |     |     | 0.15|

This means: the sample space is the Cartesian product \(\{a, b, c, d, e, f\} \times \{X, Y, Z\}\) and the probability of a pair is the corresponding number in the table. So pair aY (or (a, Y) if you prefer) is assigned probability 0 here, for example (the entry in row a, column Y).
Transcribed Image Text:**Problem 4:** Fill in the blanks to make a probability model whose "marginal probabilities" are those in the previous problem, if this is possible. If not, explain why not. **Table:** | | X | Y | Z | |---|-----|-----|-----| | a | 0.1 | | | | b | | | | | c | 0 | | 0.01| | d | 0.05| | | | e | | 0 | | | f | | | 0.15| This means: the sample space is the Cartesian product \(\{a, b, c, d, e, f\} \times \{X, Y, Z\}\) and the probability of a pair is the corresponding number in the table. So pair aY (or (a, Y) if you prefer) is assigned probability 0 here, for example (the entry in row a, column Y).
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