Variable having the standard normal distribution

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Use the result of part (b) of Exercise 20 to show that

is a value of a random variable having the standard normal distribution. Also, use the first part of Theorem 3 and the fact that are independent to show that

is a value of a random variable having the t distribution with n - 2 degrees of freedom.

Exercise 20

Under the assumptions of normal regression analysis, show that

(a) the least squares estimate of α in Theorem 2 can be written in the form

(b) has a normal distribution with

Theorem 2

Reference no: EM131137461

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