Now, the above described the parameters. What about local variables? Local variables will be declared directly after the PROCEDURE blah (...), so in this case, "c" is a local variable. The …

1. (Law of Iterated Expectation) E(X) = E[E(X | Y )]. 2. var(X) = E[var(X | Y )] + var[E(X | Y )]. These properties are useful when deriving the mean and variance of a random variable that …

To find the mean and variance, we could either do the appropriate sums explicitly, which means using ugly tricks about the binomial formula; or we could use the fact that X is a sum of n …

Polling Example 2: 100 people are chosen at random and asked if they prefer B or K; 62 say K. What is the probability that between 52% and 72% actually support K? Let X be the random …

VaR answers the question, “how much can I lose with x% percent probability over a set horizon?” For instance, a VaR of 10 million dollars at a 95% confidence level and a 1 day horizon means …

VAR(p) More generally, a p-th order reduced-form VAR is zt = 1zt 1 + 2zt 2 + : : : + φ φ φ For a bivariate system, zt is a 2 1 vector, and i; (i = 1; φ Rigorously speaking we need to choose a …

Assume we have an estimate of density D ^ and its conditional sampling variance, ^var( D ^ ). We want to multiply this by some constant c to make it comparable with other values from the …