Moments Generating Function (week 6)

Question 1

Skewness formula

Answer 1

E(Z)^3
Z liat last week

Question 2

Excess kurotsis formula

Answer 2

E(Z)^3 - 4

Question 3

+ Skewness means?

Answer 3

right tail

Question 4

Measure heaviness of distribution?

Answer 4

Excess kurtosis

Question 5

a. k-th moment of X
b. k-th central moment of X
c. k-th standarised moment of X

Answer 5

a. E(X^k)
b. E(X-µ)^k
c. E(Z)^k

Question 6

properties of MGF

Answer 6

1. 2 RV has same MGF means they identical dist
2. If X had MGF M(t), then a+bX has MGF e^(at) M(bt)
3. MGF of a sum of independent RV is a product of their MGF

Question 7

how to compute MGF?

Answer 7

1. know the PMF
   2.Mx(t) = E(E^tx)
   if discrete, Sigma e^tk Px(k)
   if continuous, Integral max infinity, min negative infinity e^(tk) fx(x)dx
2. then, derive then n and set t =0
3. keep deriving if u want to find X^2 ya derive 2 times

Question 8

Joint dist properties:

Answer 8

a. joint PMF are non-neg
b. sigma x sigma y Px,y (x,y) = 1

Question 9

Conditional probabilty of :
discrete
a. Bayes
b.LOTP

Answer 9

a. P(Y|X) = [P(X|Y)P(Y)]/P[X]
b. P(X) = Sigma P(X|Y) P(Y)

Question 10

Conditional prob of:
continuous
a. Bayes
b. LOTP

Answer 10

a.bayes the same,
b. f(x) = LOTP use integral -infinity to infinity of F(x|y)fydy