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STAT 400
Spring 2012
Homework #7
(due Friday, Mar 16th, by 3:00 p.m.)
No credit will be given without supporting work.
1.
Suppose Jane has a fair 4sided die, and Dick has a fair 6sided die.
Each day,
they roll their dice (independently) until someone rolls a “1”.
(Then the person
who did not roll a “1” does the dishes.)
Find the probability that …
a)
they roll the first “1” at the same time (after equal number of attempts);
b)
it takes Dick twice as many attempts as it does Jane to roll the first “1”;
c)
Dick rolls the first “1” before Jane does.
2.
At Sam’s Butcher Shop, ground beef packages vary in weight according to a normal
distribution with a mean of 3.1 pounds and a standard deviation of 0.2 pounds, and are
sold for $1 per pound.
Packages of Bratwurst vary in weight according to a normal
distribution with a mean of 2.6 pounds and a standard deviation of 0.3 pounds, and are
sold for $3 per pound.
Anticipating nice weather during the weekend, Dick buys
two
packages of ground beef and
one package of Bratwurst, selecting the packages at
random.
What is the probability that Dick would exceed the $15 limit “suggested”
by his wife Jane?
(
Assume independence.
)
3.
Let
X
and
Y
have the joint probability density function
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This note was uploaded on 03/14/2012 for the course STAT 400 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Kim
 Statistics, Probability

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