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Exercise 4 In Neverland, annual income (in $), X, is distributed according to a

ID: 3059471 • Letter: E

Question

Exercise 4 In Neverland, annual income (in $), X, is distributed according to a Garnma distribution with a = 5 and 10.000. Every year, the IRS audits 1% of the individuals with an income below $50,000, 3% of individuals with incomes between $50,000 and $95,000, and 6% of individuals with an income above 95,000. Suppose that the individuals to be audited are selected at random (a) What is the distribution of the income groups? That is, what proportion of Neverland's population falls into each of the three incorne groups? Even more specifically, find PA $50,000), PSD,000 's95,000), and P(X > $95,000). Hint: These probabilities should add to 1 (b) You overhear Mr. Statman complain about being audited. What is the probability that Mr. Statman's income is below $50,000? Between $50, 000 and $95,000? Above $95,000? of Mr. Statman's possible income (group) given that he's being audited

Explanation / Answer

Exercise 4 In Neverland, annual income (in $), X, is distributed according to a Garnma distribution with a = 5 and 10.000. Every year, the IRS audits 1% of the individuals with an income below $50,000, 3% of individuals with incomes between $50,000 and $95,000, and 6% of individuals with an income above 95,000. Suppose that the individuals to be audited are selected at random (a) What is the distribution of the income groups? That is, what proportion of Neverland's population falls into each of the three incorne groups? Even more specifically, find PA $50,000), PSD,000 's95,000), and P(X > $95,000). Hint: These probabilities should add to 1 (b) You overhear Mr. Statman complain about being audited. What is the probability that Mr. Statman's income is below $50,000? Between $50, 000 and $95,000? Above $95,000? of Mr. Statman's possible income (group) given that he's being audited