It is well known that a standard normal random variable N(0, 1) divided by a square root of a chisquared random variable divided by its degrees of freedom (χ2

ν/ν) 12 results in a random variable that is t-distributed with ν degrees of freedom, provided the N(0, 1) and the χ2 variables are independent, see Chapter 2. Use this fact to show that (βOLS

− β)/[s/(

n i=1 x2i

) 1 2 ] ∼ tn−2.