C2. For each of the following, (a) calculate the exact value using R; (b) get an approximate value using an appropriate approximation and without using R. (Statistical tables are available.) (i) P(X < 3), where X - Bin(1000, 0.005). (ii) P(190 < Y < 205), where Y ~ Bin(500, 0.4). (iii) P(Z > 398), where Z - Bin(400,0.999).
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- The linearization of ex at x = 1 Estimate to five decimal places the magnitude of the error involved in replacing ex by 1 + x on the interval [0, 0.2]With α = .05 and df = 8, the critical values for a two-tailed t-test are t = ±2.306. Assuming all other factors are held constant if the df value were decreased to df = 5, what would happen to the size of the critical regions?In an effort to make the distribution of income more nearly equal, the government of a country passes a tax law that changes the Lorenz curve from y = 0.98x2.1for one year to y = 0.32x2 + 0.68x for the next year. Find the Gini coefficient of income for both years. (Round your answers to three decimal places.) after before
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