Please complete the following questions

Show transcribed image text Problem 1. (25 pts) A set of samples x1, x2,..xn is taken from a random variable X uniformly distributed over [O, bl. The upper limit, b is known (a) Use moment estimator (ME) to estimate b. (b) Use maximum likelihood estimator (MLE) to estimate b. Problem 2. (25 pts) A set of samples x1, x2,..xn is taken from a random variable X uniformly distributed over [a, b]. Both a, and b, are known. (a) Use moment estimator (ME) to estimate a and b (b) Use maximum likelihood estimator (MLE) to estimate a and b Problem 3: (50 pts) Two additional estimators can be constructed in the following manner for problem 1: b3-min(x1, x2… Xn)+max(x1, x2, .. Xn); b4: If ME result is smaller than MLE result,take MLE result. If ME result is larger than MME, take the mean of ME and MME results. Of the four estimators (ME, MLE, b3 and b4), rank your preferences with reason. Write a matlab program to compare the four estimators. Discuss their pros and cons. Are your preferences justified? Do this for n-10 and n-100;

Problem 1. (25 pts) A set of samples x1, x2,..xn is taken from a random variable X uniformly distributed over [O, bl. The upper limit, b is known (a) Use moment estimator (ME) to estimate b. (b) Use maximum likelihood estimator (MLE) to estimate b. Problem 2. (25 pts) A set of samples x1, x2,..xn is taken from a random variable X uniformly distributed over [a, b]. Both a, and b, are known. (a) Use moment estimator (ME) to estimate a and b (b) Use maximum likelihood estimator (MLE) to estimate a and b Problem 3: (50 pts) Two additional estimators can be constructed in the following manner for problem 1: b3-min(x1, x2… Xn)+max(x1, x2, .. Xn); b4: If ME result is smaller than MLE result,take MLE result. If ME result is larger than MME, take the mean of ME and MME results. Of the four estimators (ME, MLE, b3 and b4), rank your preferences with reason. Write a matlab program to compare the four estimators. Discuss their pros and cons. Are your preferences justified? Do this for n-10 and n-100;