Statistics for Econometrics

Statistics for Econometrics
Assignment 2
Instructions
Total weight in final assessment: 10%.
Marking: Marks will be awarded for correct working and explanation as well as correct
final answers. Students are allowed to work in groups. However, each student MUST
hand in their own work in their own words.
Assignment: The assignment must be produced using an appropriate wordprocessor (no
handwritten assignments are accepted) and should preferably be submitted as a PDF. The
assignment (both electronic and hard copies) must have a completed and signed official
cover sheet as the first page. This can be found on the course website in the “course
documents” folder.
Questions
1. (a) Suppose that a random variable X can have each of the seven values
-3, -2, -1,0, 1, 2,3
with equal probability. Determine the p.m.f. of Y = X 2 – X.
(b) Determine the p.d.f. of Y = 4 – X3, if the p.d.f. of random variable X is

2 5:10 for 0 < a: < 2,
f { 0 otherwise.
(0) Find the p.d.f. of Z = X/Y, if the random variables X and Y have the joint
p.d.f. given by
2(r13-l-y) foro§m§y§1,
f (m’y) – { 0 otherwise.
2. Suppose that X1, . . . ,Xn form a random sample of size n from a Beta distribution
with parameters 04 and fl = 1 and p.d.f. given by
f($loz)=oz:ca’1, 0§xglg 0<a<oo.

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