STAT 400
Spring 2011
Homework #8
(due Thursday, March 17, by 4:30 p.m.)
No credit will be given without supporting work.
1.
Dick and Jane have agreed to meet for lunch between noon (0:00 p.m.) and
1:00 p.m.
Denote Jane’s arrival time by X, Dick’s by Y, and suppose X and Y
are independent with probability density functions
( )
≤
≤
=
otherwise
0
1
0
3
2
X
x
x
x
f
( )
≤
≤
=
otherwise
0
1
0
2
Y
y
y
y
f
Find the probability that Jane arrives before Dick.
That is, find
P
(
X < Y
).
2.
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.
3.
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 Spring '08
 
 Normal Distribution, Standard Deviation, DICK, Probability theory, probability density function

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