Exercise 10. Suppose X1, X2, · , Xn is an i.i.d. sample of observations ofN(u, o?), show thata random variable X2~n5 (X; - 4)?~x(n)(32)i=1Exercise 11. Suppose X1, X2,... , Xn is an i. i.d. sample of observations ofa random variable X N(u, o²), and X is the sample mean. Show that(X - 4)?~x²(1)(33)o2Take care to give a complete explanation, using only those results that havebeen established!14

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Answered: ~x(n) (32) i=1 Exercise 11. Suppose X1,…

A First Course in Probability (10th Edition)

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~x(n) (32) i=1 Exercise 11. Suppose X1, X2,.,Xn is an i.i.d. sample of observations of a random variable X ~ N(u, o2), and X is the sample mean. Show that (X – µ)² ~x°(1) (33) o2 Take care to give a complete explanation, using only those results that have been established! 14