# Tutor profile: Zara K.

## Questions

### Subject: Statistics

Use the mgf to verify that E(X^2)= m''(0) = 1 and E(X^4)= m''''(0) = 3. Assume normal standard distribution.

m′(t) =t*e^(1/2*t^2), m′′(t) = (t^2+ 1)*e^(1/2*t^2), m'''(t) = (t^3+ 3t)*e^(1/2*t^2) ,m'''(t) = (t^4+ 6*t^2+ 3)*e^(1/2*t^2) Thus, E(X^2) =m′′(0) = (0 + 1)*1 = 1, E(X^4) =m''''(0) = (0 + 0 + 3)*1 = 3.

### Subject: Algebra

If x <3, simplify |x - 3| - 5*|-7|

If x < 3 then x - 3 < 0 and if x - 3 < 0 the |x - 3| = -(x - 3). Substitute |x - 3| by -(x - 3) and |-7| by 7 . |x - 3| - 5*|-7| = -(x - 3) -5*(7) = -x -32

### Subject: Microeconomics

Solve the Consumer Problem and state the Marshallian demand for the following utility function: u(x) =x1+x2

since ∂u/∂x1=∂u/∂x2= 1, ifp1 is not equal p2, the consumer optimizes by spending all his wealth on whichever good is cheaper; if p1=p2, any mixture of the two goods which exhauststhe budget gives the same utility. So, x(p,w) = (0,w/p2) if p1> p2 x(p,w) = {(aw/p1,(1−a)w/p2) : a∈[0,1]} if p1=p2 x(p,w) = (w/p1,0) if p1< p2