A2soln2 - Assignment 3 MATBUS 472 Due April 2 at the beginning of class 1 The probability density function for an exponential distribution is e-x where

# A2soln2 - Assignment 3 MATBUS 472 Due April 2 at the...

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Assignment 3 MATBUS 472 Due April 2 at the beginning of class 1. The probability density function for an exponential distribution is e - x where x is the value of the variable and _ is a parameter. The cumulative probability distribution is 1− e - x . Suppose that two variables V 1 and V 2 have exponential distributions with parameters of 1.0 and 2.0, respectively. Use a Gaussian copula to define the correlation structure between V 1 and V 2 with a copula correlation of 0.2. Produce a table similar to Table 11.3 using values of 0.25, 0.5, 0.75, 1, 1.25, and 1.5 for V 1 and V 2 . A spreadsheet for calculating the cumulative bivariate normal distribution is on the author’s website: ronto.ca/ hull. The probability that V 1 < 0.25 is 1 e 1.0×0.25 = 0.221. The probability that V 2 < 0.25 is 1 e 2.0×0.25 = 0.393. These are transformed to the normal variates 0.768 and 0.270. Using the Gaussian copula model the probability that V 1 < 0.25 and V 2 < 0.25 is M (−0.768,−0.270,−0.2) = 0.065. The other cumulative probabilities are shown in the table below and are calculated similarly.

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