Recall figures 15.4 and 15.5. Assume that i and j are both normally distributed with E(i) =
Question:
Recall figures 15.4 and 15.5. Assume that εi and εj are both normally distributed with E(εi) = 0 and V(εi) = 36,000,000.
(a) If we were to choose b = 6,000 and a = −28,000, what would P(yi < 50,000)
be? What would P(yj > 50,000) be? What would P(yi < 50,000) ×
P(yj > 50,000) be?
(b) If we were to choose b = 9,000 and a = −108,000, what would P(yi <
50,000) be? What would P(yj > 50,000) be? What would P(yi < 50,000) ×
P(yj > 50,000) be?
(c) If we were to choose b = 12,000 and a = −94,000, what would P(yi <
50,000) be? What would P(yj > 50,000) be? What would P(yi < 50,000) ×
P(yj > 50,000) be?
(d) Based on your answers to parts b and
c, what would happen to P(yi <
50,000) × P(yj > 50,000) if we chose even larger values of b and even smaller values of a? Are there many pairs of values for b and a that would yield essentially the same value for P(yi < 50,000) × P(yj > 50,000)? Why or why not?
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