By Robert C. Higgins
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Additional info for Analysis for Financial Management 8th Ed. (McGraw-Hill Irwin Series in Finance, Insurance, and Real Est)
1 where yi = 0, 1, 2, . . and E(yi ) = Var(yi ) = λ, and λ is the unknown parameter that is to be estimated. • Derive the likelihood function for λ. Are there any terms that can be dropped due to the proportionality property? • Derive the log-likelihood function and the score for λ. Conﬁrm that the expected score at the true parameter λ0 is equal to zero.
Two random variables X and Y are independent if, and only if f (x, y) = f (x)f (y) or, equivalently, X and Y are independent if f (x|y) = f (x) or f (y|x) = f (y). If X and Y are not statistically independent, then they are called statistically dependent. Statistical independence has two important implications. First, if we know the outcome of X, this additional information does not change the probability of observing a particular value of Y . Second, if X and Y are independent, then any two functions h(X) and g(Y ) are independent as well.
Each mean can be interpreted as an estimator for the true average in that year, and thus for the expectation conditional on the survey year, denoted by E(yi |yeari ). 36 between 1986 and 2002, and this decline is statistically signiﬁcant. We cannot tell from this mean comparison, however, what changes in the fertility distribution were responsible for the average decline. For example, the decline could result either from an increase in the number of childless women, or from a decline in the proportion of very large numbers of children.
Analysis for Financial Management 8th Ed. (McGraw-Hill Irwin Series in Finance, Insurance, and Real Est) by Robert C. Higgins