TABLE OF CONTENTS | 1. | Calculate (3.3), (3.4) and (3.5) in case N has the following distribution: a) Poisson( ?), b) binomial( n, p) and c) negative binomial( r, p). |
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| 2. | Give the counterpart of (3.5) for the cumulant generating function. |
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| 3. | Assume that the number of eggs in a bird's nest is a Poisson( ?) distributed random variable, and that the probability that a female hatches out equals p. Determine the distribution of the number of females in a bird's nest. |
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| 4. | Let S be compound Poisson distributed with ? = 2 and p( x) = x/10, x = 1, 2, 3, 4. Apply (3.10) to calculate the probabilities of S = s for s ? 4. |
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| 5. | Complete the table in Example 3.2.2 for x = 0, , 6. Determine the expected value and the variance of N, X and S. |
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| 6. | Determine the expected value and the variance of S, where S is defined as in Example 3.2.2, except that N is Poisson distributed with ? = 2. |
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| 7. | Prove relation (3.11) by partial integration. Do the same by differentiating both sides of the equation and examining one value, either x = 0 or x ? ?. |
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Answers
| 1. | For Poisson ( ?): E[ S] = ? ? l, Var[ S] = ? ? |
