MATH 302 WORKSHEET 1
e
SPRING 2012
2
Note:
Theorem 3 : Let X ~ Nor (x, ,). Let Z =
X
it is the case that Z ~ Nor (z, 0, 1).
2
Theorem 4: Let Z ~ Nor (z, 0, 1). Let Y = Z2 it is the case that Y ~ 1 .
Theorem 4 : Let X ~ 2 and Y ~ 2 and X and Y be independ
MATH 302 WORKSHEET 5 SPRING 2012
If something does not exist write DNE and explain why it does not exist.
1. Let X, Y be jointly distributed such that the joint probability mass function, kxy(x, y) is defined as:
x + y
x 3 y 2
kxy(x, y) = 21
0
else
A. Fin
Math 302 Section 010 - P. & S II - Dr. McLoughlin - Spring of 2012 - Worksheet Four
Worksheet 4 1
2
Homework of 2012-02-14
Dr. M. P. M. M. McLoughlin
Spring of 2012
1. Do problems 4, 5 on worksheet4
2. Do problems 1, 3, 5 on worksheet5
3 . Let X, Y Dir(x,
Math 302 Section 010 - P. & S II - Dr. McLoughlin - Spring of 2012 - Worksheet Four
Worksheet 4 1
e
Homework of 2012-02-12
Dr. M. P. M. M. McLoughlin
Spring of 2012
1. Prove the following claims (all are board - worthy ( ):
(1) Theorem 3 of Handout 0.1 of
MATH 302 WORKSHEET
SPRING 2012
e
is the same as theorem 19 of Hand-out 3.
2
Note: Theorem 2.6 of Hand-out 2 is the same as theorem 4 of Hand-out 3.
e
There are other repetitions of theorems between and betwixt hand-outs 1 2 , 2, and 3. Sometimes
repetiti
MATH 302 PROB. & STATS II WORKSHEET 1
NAME:_
(PLEASE PRINT LEGIBLY)
If an answer does not exist explain why it does not exist.
1. Let X,
Y be jointly distributed such that the joint probability mass function, kxy(x, y) is defined as:
x y
x 3 y 2
kxy(x, y
Math 302 Section 010 - P. & S II - Dr. McLoughlin - Spring of 2012 - Worksheet One
1
Worksheet 1 4
Homework & Claim
Dr. M. P. M. M. McLoughlin
Spring of 2012
1. (Mr. OConnors Claim) Prove or disprove.
Let g (x, y ) be a well dened joint probability functi
MATH 302 WORKSHEET VI SPRING 2012
NAME:_
(PLEASE PRINT LEGIBLY)
1. Let X1 be a random sample from a N(x, X,
X) such that X = 40 and 2 =64. Find the approximate Pr(X > 44).
X
X2, X3, X4 , X5 be a random sample from a N(x, X, X) such that X = 40 and 2 =64.
MATH 302 WORKSHEET V SPRING 2009
NAME:_
(PLEASE PRINT LEGIBLY)
1. Let X, Y be jointly distributed such that the joint probability density function, fxy(x, y) is defined as:
12xy(1 y) 0 < x < 1 0 < y < 1
fxy(x, y) =
0
else
A. Find the conditional p. d. f.
MATH 302 WORKSHEET 3 SPRING 2009
NAME:_
(PLEASE PRINT LEGIBLY)
JOINT PROBABILITY MASS FUNCTIONS,
CONDITIONAL PROBABILITY MASS FUNCTIONS,
VERSUS MARGINAL PROBABILITY MASS FUNCTIONS.
1. Let X, Y be jointly distributed such that the joint probability mass fu
MATH 302 PROBS. & STATS II WORKSHEET I 2010-01-19 NAME:_
(PLEASE PRINT LEGIBLY)
Use pencil only. Limited partial credit. All the necessary & sufficient steps for a proof should be shown - further,
justification for each step should be provided. If there i
Math 302, Dr. McLoughlin, Worksheet I, page 1 of 3
MATH 302 WORKSHEET IV SPRING 2010 NAME:_
(PLEASE PRINT LEGIBLY)
3 2
x (1 y ) 1 x 1, 1 y 1
1. Let X, Y ~ w(x,y) such that w(x,y) = 2
0
else
2
A. Find X
B. Find Y
C. Find X
D. Find XX
E. Find XY
2. Let X,
Math 302, Dr. McLoughlin, Worksheet I, page 1 of 3
MATH 302 WORKSHEET II
SPRING 2009
NAME:_
(PLEASE PRINT LEGIBLY)
3 2
x (1 y ) 1 x 1, 1 y 1
1. Let X, Y ~ k(x,y) such that k(x,y) = 2
0
else
A. Show that k(x,y) is a well defined joint probability density
MATH 302 PROBS. & STATS II WORKSHEET 0 2012-01-19 NAME:_
(PLEASE PRINT LEGIBLY)
Use pencil only. All the necessary & sufficient steps for a proof should be shown - further, justification for each
step should be provided. If there is no work shown - no cre
Math 302, Dr. McLoughlin, Worksheet I, page 1 of 3
MATH 302 WORKSHEET III
SPRING 2009 NAME:_
(PLEASE PRINT LEGIBLY)
3 2
x (1 y ) 1 x 1, 1 y 1
1. Let X, Y ~ k(x,y) such that k(x,y) = 2
0
else
A. Find kX(x)
B. Find kY(y)
C. Find E[X]
D. Find E[Y]
E. Find E