a.
Calculate the values of
a.
Answer to Problem 104E
The value of
The value of
Explanation of Solution
Calculation:
The possible values of
1 | 0 | 1 | |
1 | 1 | 0 | |
2 | 0 | 2 | |
2 | 1 | 1 | |
2 | 2 | 0 | |
3 | 0 | 3 | |
3 | 1 | 2 | |
3 | 2 | 1 | |
3 | 3 | 0 | |
Total | – | – | 1 |
Extracting the unique values of Y from the above table, and adding up all the probabilities corresponding to that value gives the probability distribution of
1 | |
2 | |
3 | |
Total | 1 |
Thus,
Thus, the value of
Again,
Thus, the value of
b.
Calculate the values of
b.
Answer to Problem 104E
The value of
The value of
Explanation of Solution
Calculation:
Hypergeometric distribution:
A discrete real valued random variable Y is said to follow hypergeometric distribution if the probability mass
Where integer y takes value from 0, 1, 2,…, n with the conditions
Consider that
Then, the marginal probability functions of
The joint probability distribution of
Thus, the marginal probability distribution of
Thus, the marginal probability distribution of
Now, the marginal probability distribution of
Thus, marginal probability distribution of
For a random variable,
Thus, the value of
Thus,
Thus, the value of
Again, the value of
From Exercise 5.90, the value of
Thus,
Thus, the value of
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Chapter 5 Solutions
Mathematical Statistics with Applications
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