1. Consider the following short-run model: Y a, - b ( Re - F) a Y - 6. YY EX IM. aim Yt, where C is consumption at time t, It is investment, G, is government purchases, EX, and IM, are exports and imports, Y, is potential output, Y is short-run output, R, is the real interest rate, 7 is the marginal product of capital, and as, di, ag, der, dim, 61, and 62 are parameters. (a) Derive the equation for the IS-curve (that is, the relationship between short-run output and the real interest rate) when 61 6 [0, 1) and 62 2 0. (b) Draw the IS-diagram (that is, the diagram with the real interest rate on the vertical axis and short-run output on the horizontal axis) with two IS-curves. The first IS-curve is given by the answer to part a) when o, = 0 and 62 = 0. The second IS-curve is given by the answer to part a) when 0 61. Suppose the real interest rate increases. Show graphically what will happen to short-run output for both IS-curves. Carefully explain why short-run output is more sensitive to changes in the real interest rate in one of the models.Statistical Inference: One Population Binomial Distribution Hypothesis Testing 1. Consider drawing a random sample of size n = 100 of a random variable X that has a Bernoulli distribution with probability of success p = .75. (a) What is P(p 2 .98)? Note that this can be answered with an approximation or with an exact value. If you are using an approximation, explain why the approximation is valid. (b) What is P(p