1
Q
How can you know the distribution through the MGF technique?
A
- Find the MGF of Y
- Compare the MGF of Y with other well-known MGFs. If its MGF is the same as the MGF of U, then Y and U have identical density functions
2
Q
If X~N(mu, sigma^2) then Y = aX + b. What distribution does it follow?
A
Norma distribution with E(Y) = amu + b and Var(Y) = a^2sigma^2
3
Q
if Z~N(0,1) what distribution does Z^2 follow?
A
Chi-squared distribution with k=1
4
Q
Steps in CDF technique
A
- If not given, derive the CDF of X
- Express the CDF of Y in terms of the CDF of X
- If asked for, derive the PDF of Y
5
Q
Steps for MTD continuous case 1-to-1 mapping and Y is monotonically increasing or decreasing
A
- Find the inverse of g(y) and its derivative with respect to y
- Derive the density function f(y) = f(g inverse)|derivative of g inverse|
6
Q
Steps for MTD continuous case NOT 1-to-1 mapping
A
- Partition A into a finite or countable number of sets s.t. Y = g(X) defines a 1-to-1 transformation
- For each set in the partition find the inverse of g and its derivative
- Derive the density function f(y) = summation of F(inverse of g)|derivative of inverse g| from 1 to n
