Let x be a binary explanatory variable and suppose P(x = 1) = for 0 <

Let x be a binary explanatory variable and suppose P(x = 1) = ρ for 0 < ρ < 1.

(i) If you draw a random sample of size n, find the probability—call it γ_n—that Assumption SLR.3 fails.

(ii) If ρ = 0.5, compute the probablity in part (i) for n = 10 and n = 100. Discuss.

(iii) Do the calculations from part (ii) with ρ = 0.9. How do your answers compare with part (ii)?