Answer Happy

(i) Analytical values of quantiles for exponential distribution with mean u and variance o2 can be computed as: In(1-P) 4p 1 . Using definitions of quantile function and exponential CDF, derive the above formula . Using this expression, compute the quartiles for Exp(5). • Verify the results graphically using area (). • Verify the results using expinv(). (ii) The normal distribution CDF and its inverse are not available in closed form, and CDF-1 computation requires careful use of numerical procedures. In probability theory and statistics, the probit function is the quantile function associated with the standard normal distribution. In computing environments where numerical implementations of the inverse error function are available, the probit function may be obtained as: probit(p) = verf-(2p - 1). Because the normal distribution is from location-scale family, its quantile function for arbitrary parameters can be derived from a simple transformation of the quantile function of the standard normal distribution (the probit function). Analytical values of quantiles for normal distribution with mean u and variance o can be computed as: qp = + ovZ erf-(2p - 1) Using this expression, compute the quartiles for N (5,5). Verify the results graphically using normspec(). • Verify the results using norminv().