Homework 10/30 October 24 2011 1. For X pareto with parameters x0 = 1; > 1 ( see

Homework 10/30 October 24 2011 1. For X pareto with parameters x0 = 1; > 1 ( see inside back cover of text) let be the mean of the distribution and compute PfX > g and also lim!1PfX > g. 2. 5.10.2 Suppose on test A the mean is 85 and the st.dev. is 10 and on test B the the mean is 90 and the st.dev. is 16. Suppose that the scores on the two exams are jointly normal with correlation .8. If a student scores 80 on test A what is the probability that she will score more that 90 on test B ? Remark: to test your intuition rst ask yourself if it is bigger or smaller that .5. 3. 5.10.
Homework 10/30 October 24 2011 1. For X pareto with parameters x0 = 1; > 1 ( see inside back cover of text) let be the mean of the distribution and compute PfX > g and also lim!1PfX > g. 2. 5.10.2 Suppose on test A the mean is 85 and the st.dev. is 10 and on test B the the mean is 90 and the st.dev. is 16. Suppose that the scores on the two exams are jointly normal with correlation .8. If a student scores 80 on test A what is the probability that she will score more that 90 on test B ? Remark: to test your intuition rst ask yourself if it is bigger or smaller that .5. 3. 5.10.6 Suppose X and Y are joint normal with covariance matrix and mean . Compute the value of b for which 2(X??bY ) will be a minimum. 4. Let be one on the diagonal and a constant r; 0 r 1 othe diagonal. These normals are exchangeable. Figure out an easy way to sample from this distribution.Also use R to compute a 3 dimensional example of the cholesky decomposition when the constant correlations are .4. Note that this does not give you the same method for creating your exchangeable normals. 1
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