Question: 7. (20 points) Let X be a lognormal random variable, i.e., X LogNormal(, 2). Consider a random sample of size = 20 drawn from

7. (20 points) Let X be a lognormal random variable, i.e., X

7. (20 points) Let X be a lognormal random variable, i.e., X LogNormal(, 2). Consider a random sample of size = 20 drawn from the distribution of X and given. as below: 27 82 115 126 155 161 243 249 340 348 457 680 855 877 974 1,193 1,340 1,884 2,558 15,743 (a) (5 points) (b) (5 points) Find the Fisher information matrix I(1,7). (c) (5 points) Find the variance-covariance matrix Cov(1,8). (d) (5 points) Compute the 95% symmetric confidence intervals for both parameters and a. Find the MLE's and 7 of u and o, respectively.

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