The following BASIC code generates 10,000 values of a random variable Y, which is the sum X1+X 2. In cases


The following BASIC code generates 10,000 values of a random variable \(Y\), which is the sum X1+X 2. In cases 1 , 2 , and 4 , assume that X1 and X2 are independent realizations of the same random variable X. In case 3 , assume that X1 has the same uniform distribution as in case 1 , and that X 2 is described by the density function specified (and X1 and X2 are independent). The program calculates the sample average, the sample variance, and the fraction of sample values Y that are less than or equal to 1/2. Adapt this simulation program (you may use BASIC or any other language) to calculate the values required to fill in the table for E(Y), V(Y), and P(a<Y ≤ b), where a and b are specified in Homework 0. In each case, show all theoretical calculations for E(Y), V(Y) and P(a<Y ≤ b).

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