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Unformatted text preview: CE 93 Joan Walker, Spring 2011 Lab 7
1. Use matlab to study the joint probability mass function
Define:
X: the number of passengers alighting at bus stop A;
Y: the number of passengers boarding at bus stop A;
Joint PMF of X and Y, pXY(x,y)=p(X=x Y=y) is known as
Y
0
1
2
3
pX(x) X 0
0.03
0.05
0.03
0.01 1
0.08
0.20
0.12
0.03 2
0.06
0.10
0.12
0.04 3
0.03
0.05
0.03
0.02 pY(y) i) Do the following conditions hold? Must they hold for the above data to represent a joint PMF?
a.
b.
ii) Compute the following marginal PMF’s. List the results in the table above.
a.
b.
iii) In Matlab, make bar graphs of the marginal PMF’s.
iv) Do the following conditions hold?
a.
b.
v) Compute the conditional probability that y people will get on the bus given that x passengers
get off, i.e.
Y
0
1
2
3 . Record the values in the table below.
X 0 1 2 3 CE 93
vi) Make bar graph of
pY(y) in iii)? Joan Walker, Spring 2011
. Do these bars look like 2. This problem does not require the use of matlab.
Two random variables X and Y have a joint PDF i) Sketch the xy plane and indicate on it the region where is nonzero. ii) Find the value of c.
iii) Find the marginal pdf fY(y).
iv) From your answer to part iii), find E[Y]
v) What is fYX(ya), the conditional pdf of Y given that X=a where 0<a<0.5?
vi) What is fYX(ya), the conditional pdf of Y given that X=a where 0.5<a<1? ...
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This note was uploaded on 06/02/2011 for the course CIV ENG 93 taught by Professor Staff during the Spring '08 term at University of California, Berkeley.
 Spring '08
 Staff

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