Name (1 pt):
ECEn 370
Quiz 13 Solutions
Monday, April 11, 2011.
The following Markov chain with transitions every hour represents a newborn baby:
1
1
0.3
2
0.7
3
0.6
4
0.4
birth
awake
eating
sleeping
1
1. How many transient states are in this Markov chain

Name:
ECEn 370
Quiz 11 Solutions
Friday, March 18, 2011.
Hints:
Convergence in probability: limn P (|Yn a| ) = 0
Central Limit Theorem: limn P X1 +Xn n z = (z )
n
1. Consider a sequence of independent random variables Xn that are uniformly distirbuted in

Name:
ECEn 370
Quiz 10 Solutions
Friday, March 18, 2011.
Law of Iterated Expectations: E [E [X |Y ] = E [X ]
Law of Total Variance: var(X ) = E [var (X |Y )] + var (E [X |Y ])
Sum of Random Number of Independent Random Variables:
E [Y ] = E[N ]E[X ]
var (

Name:
ECEn 370
Quiz 8 Solutions
Friday, March 11, 2011.
1. You have a joint PMF of
and
X
given by the following points (x, y) with
Y
1
a probability of 6 : (1, 1), (1, 2), (3, 4),
1
a probability of 2 : (-1, -2)
a) Find E[X ].
E[X ]
= 1 (1 + 1 + 3) + 1 (1

Name:
ECEn 370
Quiz 8 Solutions
Friday, March 4, 2011.
1. (7 points) Let
X
be a random variable, uniformly distributed in the interval [0, 2]. Let
distributed in the interval [0, 1].
X
and
Y
are independent. Find the PDF of
You can either use convolution

Name:
ECEn 370
Quiz 7 Solutions
Friday, February 25, 2011.
1. You have the following joint PDF with a constant density,
fX,Y (x, y ) =
2
3 , in the shaded region:
y
1
2
1
a) Find the marginal PDF,
fY ( y ) =
3y
2y
x
fY (y ).
3y
cdx = [cx]2y = c [3 y 2y ]

Name:
ECEn 370
Quiz 6 Solutions
Friday, February 18, 2011.
1. You have the following joint PDF with a constant density,
fX,Y (x, y ) = c,
in the shaded region:
y
1
2
1
x
3
a) Find c.
1
Area: 2
(3) (1) =
3
2
c=
2
3
b) Find the marginal PDF,
fY (y ) =
3y
3

Name:
ECEn 370
Quiz 5 Solutions
Friday, February 11, 2011.
1. The new fad of Greenie Babies started. There are ve plush animals. Stores of McTacoKing will give you one of the ve with
each meal purchase, but you don't know which one you will get. What is t

Name:
ECEn 370
Quiz 4 Solutions
Friday, February 4, 2011.
You have the following joint PMF of random variables
and
X
Y:
y
4
0
1/10
0
0
0
3
0
0
0
0
3/10
2
0
0
3/10
0
0
0
0
0
0
2
3
4
5
and
E[Y ],
and
1 3/10
1
1. Find the expectation and variance of
X
and
Y

Name:
ECEn 370
Quiz 3 Solutions
Friday, January 28, 2011.
1. You have an experiment where you toss three coins, each of which has a probability 2/3 of appearing heads. Suppose I have
a random variable
a) Determine
Z which
P (Z 2).
describes the total numb

Name:
ECEn 370
Quiz 2 Solutions
Friday, January 21, 2011.
1. Four students invite seven people on a group date. The probability that any one of the seven people will show up is 3 ,
4
independent of the others.
a) What is the probability that more than fou

Name:
ECEn 370 (Probabilistic Dating Analysis)
Quiz 1 Solutions
Friday, January 14, 2011.
1. You know two people, A and B, are trying to date you (exclude others), but you know they are friends and so only one of
them will try to date you at any given tim