Consider two random variables X, Y (not necessarily independent), and two real numbers a and b. Prove that Var(aX+bY) = a² Var(X)+b² Var(Y)+2ab Cov(X, Y). (Hint: Use the properties of Cov() reviewed in class.) - Prove that E[{X – E(X)}*] = E(X²) – {E(X)}², i.e., the two expressions (b) for Var(X) are indeed equivalent. (c) Prove that E[{X– E(X | Y)}² | Y] = E(X² | Y) – {E(X | Y)}², i.e., the %3D two expressions for Var(X | Y) are indeed equivalent.

Define the process of mathematical modelling?

Fill in the blank. You are doing a study for a non-profit group helping at-risk children in your city. Suppose you know that 14.2% of the children in your city live in poverty. This percentage is an example of a You are doing a study for a non-profit group helping at-risk children in your city. Suppose you know that 14.2% of the children in your city live in poverty. This percentage is an example of a population parameter. sample statistic.

Data collection methods can only be used in scientific research (A) True B False