ECON3209: Statistics for EconometricsAssignment 1

Instructions

Due date: Tuesday, March 25 (week 4).Total weight in nal assessment: 7.5%.Marking: Marks will be awarded for correct working and explanation as well as correctnal answers. Students are allowed to work in groups. However, each student MUST

hand in their own work in their own words.

Submission: Students must submit 1 hard copy AND 1 electronic copy (PDF) oftheir assignment. The electronic copy is to be submitted to the course website via

"Turnitin" by 11:59pm on the due date. Browse and upload a copy of your document -

do not paste text. Use your student ID in the le name. The hard copy (A4, your name

and ID on the cover page, stapled at top left - do not use plastic sheets or binders)

is to be submitted to the School of Economics assignment box, located on the ground

oor of the Australian School of Business building in the West wing, by 4:59pm on the

due date.

Questions

1. DeGroot, Question 6, page 54

Suppose that a box contains r red balls and w white balls. Suppose also that

balls are drawn from a box one at a time, at random, without replacement.

(a) What is the probability that all r red balls will be obtained before any white

balls are obtained?

(b) What is the probability that all r red balls will be obtained before 2 white

balls are obtained?

2. DeGroot, Question 10, page 54

Suppose that events A and B are disjoint. Under what conditions are AC and

BC disjoint?

3. DeGroot, Question 16, page 91

If ve balls are thrown at random into n boxes, and all throws are independent,

what is the probability that no box contains more than two balls?

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4. DeGroot, Question 4, page 129

Suppose that X and Y have a continous joint distribution for which the joint

p.d.f. is dened as follows:

f (x; y) =

(cy2 for 0 x 2 and 0 y 1;0 otherwise.

Determine:

(a) The value of the constant c.

(b) P (X + Y > 2)

(c) P (Y < 1=2)

(d) P (X 1)(e) P (X = 3Y ) :

5. DeGroot, Question 4, page 140

Suppose that the joint p.d.f. of X and Y is as follows:

f (x; y) =

(154x2 for 0 y 1 x2;

0 otherwise.

(a) Determine the marginal p.d.f.s of X and Y .

(b) Are X and Y independent?

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