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MAT 3172, Foundations of Probability
Solution to Assignment 4
Due on November 28, 2014
Total = 100 marks
Problem 7.51 (20 marks) The marginal density of Y is
fY (y) =
f (x, y)dy =
y ey
0 y dx
=
ey
y
y
0
= ey if y > 0
if y 0
The conditional density of X
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MAT 3172, Foundations of Probability
Solution to Assignment 1
Due date: Friday September 26, 2014
Total = 100 marks
Each problem/exercise is worth 4 marks.
Chapter 1 Problem 9. These are arrangements of 12 objects, of which 6 are of type 1, 4 are of
typ
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MAT 3172
Solutions to the Midterm Examination
October 24, 2014
Professor Raluca Balan
1. a) (15 marks) Suppose that E1 and E2 are conditionally independent given F . Then
P (E1 E2 |F )P (F )
P (E2 E1 F )
=
P (E1 F )
P (E1 |F )P (F )
P (E1 E2 |F )
=
= P
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MAT 3172, Foundations of Probability
Solution to Assignment 3
Due on November 19, 2014
Total = 100 marks
Problem 6.41 (10 marks) (a) The marginal density of X is:
fX (x) =
xex(y+1) dy = xex
0
exy dy = xex
0
1
= ex ,
x
x > 0.
The marginal density of Y is
MAT 3172, Formula Sheet
Let X1 and X2 be two random variables with the joint density function
fX1 ,X2 (x1 , x2 ) and g1 : R2 R, g2 : R2 R two functions with the following
properties:
1. The system of equations:
g1 (x1 , x2 ) = y1
g2 (x1 , x2 ) = y2
has a
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MAT 3172, Foundations of Probability
Solution to Assignment 2
Due on October 22, 2014
Total = 100 marks
Problem 6.1. (10 marks) The samples space is S = cfw_(i, j); 1 i, j 6. X (the largest value)
takes values in cfw_1, 2, . . . , 6. Y (the sum) takes v