Question 5 Suppose Xi, i = 1,...,n are independent and identically distributed ran- dom variables, and...

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Question 5 Suppose Xi, i = 1,...,n are independent and identically distributed ran- dom variables, and let Sn = Use the CLT to approximate the probability P(S t). Find out if the approximation is close to the exact probability. (You will likely need statistical computing software to obtain exact probabilities and the normal approximations. Do it in the case that: 2 a) (1 mark) t = 50, n = 25, Xi ~ Poisson (X = 2) Xi b) (1 mark) t = 100, n = 50, X; ~ Poisson(A = 2) c) (1 mark) t = 115, n = 50, Xi ~ Poisson (A = 2) d) (1 mark) t = 25, n = 25, X ~ Gamma(a = 1, = 1) e) (1 mark) t = 35, n = 25, Xi ~Gamma(a = 1, B = 1) f) (1 mark) t = 65, n = 50, X; ~ Gamma(a = 1, = 1) Question 5 Suppose Xi, i = 1,...,n are independent and identically distributed ran- dom variables, and let Sn = Use the CLT to approximate the probability P(S t). Find out if the approximation is close to the exact probability. (You will likely need statistical computing software to obtain exact probabilities and the normal approximations. Do it in the case that: 2 a) (1 mark) t = 50, n = 25, Xi ~ Poisson (X = 2) Xi b) (1 mark) t = 100, n = 50, X; ~ Poisson(A = 2) c) (1 mark) t = 115, n = 50, Xi ~ Poisson (A = 2) d) (1 mark) t = 25, n = 25, X ~ Gamma(a = 1, = 1) e) (1 mark) t = 35, n = 25, Xi ~Gamma(a = 1, B = 1) f) (1 mark) t = 65, n = 50, X; ~ Gamma(a = 1, = 1)