PROBLEM 13E

An obstetrician does ultrasound examinations on her patients between their 16th and 25th weeks of pregnancy to check the growth of each fetus. Let X equal the widest diameter of the fetal head, and let Y equal the length of the femur, both measurements in mm. Assume that X and Y have a bivariate normal distribution with μX = 60.6, σX = 11.2, μY = 46.8, σY = 8.4, and ρ= 0.94.

(a) Find P(40.5 < Y < 48.9).

(b) Find P(40.5 < Y < 48.9 |X = 68.6).

Growth Theory—10.7.2016 Solow I: Relationship between inputs and outputs in the economy Y = F(physical capital, human capital, and natural resources) First version of the model focused solely on physical capital. Why Because: o Capital resources in wealthy nations far exceed those in developing nations o Periods of investment are correlated with periods of economic expansion Marginal product – the change in output divided by the change in input. This means that the more given input, the higher the GDP. Diminishing marginal product – the marginal product of an input falls as the quantity of the input rises. Y (real GDP) Y3 Y2 Y1