3. You are given that the number of claims (N) follows a geometric dis- tribution with...

 

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3. You are given that the number of claims (N) follows a geometric dis- tribution with mean 3. Observations that are equal to zero claims and one claim have been deleted; you observe the following sample: Number of Claims | 2 | 3 | 4 | 5+ Number of Policies 62 256 0 (a) Using the probability mass function (pmf) for a geometric distribution with mean 3, show that the pmf for a "zero-one-truncated geometric distribu- tion:" where the probabilities of zero claims and one claim are each set equal to zero, and each of the other claim probabilities are scaled proportionately, can be expressed as: (148)k-1 for k = 2, 3, .... Make your argument using the conditional probability rule, starting from P= Pr(N = k|N22). Show all your steps. (b) Calculate the maximum likelihood estimate of 3. (c) Using the fitted zero-one-truncated geometric distribution, calculate the probability of three claims. PT = = 3. You are given that the number of claims (N) follows a geometric dis- tribution with mean 3. Observations that are equal to zero claims and one claim have been deleted; you observe the following sample: Number of Claims | 2 | 3 | 4 | 5+ Number of Policies 62 256 0 (a) Using the probability mass function (pmf) for a geometric distribution with mean 3, show that the pmf for a "zero-one-truncated geometric distribu- tion:" where the probabilities of zero claims and one claim are each set equal to zero, and each of the other claim probabilities are scaled proportionately, can be expressed as: (148)k-1 for k = 2, 3, .... Make your argument using the conditional probability rule, starting from P= Pr(N = k|N22). Show all your steps. (b) Calculate the maximum likelihood estimate of 3. (c) Using the fitted zero-one-truncated geometric distribution, calculate the probability of three claims. PT = = 3. You are given that the number of claims (N) follows a geometric dis- tribution with mean 3. Observations that are equal to zero claims and one claim have been deleted; you observe the following sample: Number of Claims | 2 | 3 | 4 | 5+ Number of Policies 62 256 0 (a) Using the probability mass function (pmf) for a geometric distribution with mean 3, show that the pmf for a "zero-one-truncated geometric distribu- tion:" where the probabilities of zero claims and one claim are each set equal to zero, and each of the other claim probabilities are scaled proportionately, can be expressed as: (148)k-1 for k = 2, 3, .... Make your argument using the conditional probability rule, starting from P= Pr(N = k|N22). Show all your steps. (b) Calculate the maximum likelihood estimate of 3. (c) Using the fitted zero-one-truncated geometric distribution, calculate the probability of three claims. PT = = 3. You are given that the number of claims (N) follows a geometric dis- tribution with mean 3. Observations that are equal to zero claims and one claim have been deleted; you observe the following sample: Number of Claims | 2 | 3 | 4 | 5+ Number of Policies 62 256 0 (a) Using the probability mass function (pmf) for a geometric distribution with mean 3, show that the pmf for a "zero-one-truncated geometric distribu- tion:" where the probabilities of zero claims and one claim are each set equal to zero, and each of the other claim probabilities are scaled proportionately, can be expressed as: (148)k-1 for k = 2, 3, .... Make your argument using the conditional probability rule, starting from P= Pr(N = k|N22). Show all your steps. (b) Calculate the maximum likelihood estimate of 3. (c) Using the fitted zero-one-truncated geometric distribution, calculate the probability of three claims. PT = = 3. You are given that the number of claims (N) follows a geometric dis- tribution with mean 3. Observations that are equal to zero claims and one claim have been deleted; you observe the following sample: Number of Claims | 2 | 3 | 4 | 5+ Number of Policies 62 256 0 (a) Using the probability mass function (pmf) for a geometric distribution with mean 3, show that the pmf for a "zero-one-truncated geometric distribu- tion:" where the probabilities of zero claims and one claim are each set equal to zero, and each of the other claim probabilities are scaled proportionately, can be expressed as: (148)k-1 for k = 2, 3, .... Make your argument using the conditional probability rule, starting from P= Pr(N = k|N22). Show all your steps. (b) Calculate the maximum likelihood estimate of 3. (c) Using the fitted zero-one-truncated geometric distribution, calculate the probability of three claims. PT = = 3. You are given that the number of claims (N) follows a geometric dis- tribution with mean 3. Observations that are equal to zero claims and one claim have been deleted; you observe the following sample: Number of Claims | 2 | 3 | 4 | 5+ Number of Policies 62 256 0 (a) Using the probability mass function (pmf) for a geometric distribution with mean 3, show that the pmf for a "zero-one-truncated geometric distribu- tion:" where the probabilities of zero claims and one claim are each set equal to zero, and each of the other claim probabilities are scaled proportionately, can be expressed as: (148)k-1 for k = 2, 3, .... Make your argument using the conditional probability rule, starting from P= Pr(N = k|N22). Show all your steps. (b) Calculate the maximum likelihood estimate of 3. (c) Using the fitted zero-one-truncated geometric distribution, calculate the probability of three claims. PT = =

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