Course : Analysis of experience plans MAT3378 Exercise 4: Consider a random sample 1, ... ... , with a normal distributionwith mean and variance 2. Let the following variables be : X 1 =( Y )/(/ n ),X 2 =( Y )/(s/ n ),X 3 =(n1)S 2 / 2 andX 4 =X 1 2 X 3 (a) Determine the distribution of each of the variables 1, ... , 4, specifying their parameters. their parameters. (b) Let n = 10. Using R, calculate the following probabilities: i.) (1 < 1,966) ii) (2 > 3,45) iii) (3 > 8,35) iv) (4 > 12,35)