Consider the function Y X exp (2X). Suppose the distribution of X is unknown but its mean, standard deviation, skewness coefficient and Kurtosis are known to be ux = σχ == 2 k and K = 3+, respectively. (Note: these values happen to be the properties of a gamma distribution having the parameters vand k.)
a) Fork 2 and v = 10 and 20, estimate the mean and standard deviation of Y using first and second- order approximation methods.