CSCI 1550
Randomized Algorithms and Probabilistic Analysis
1
Prof. Eli Upfal
Homework 2
DUE: 2/12/2015
Please Note:
Assignments will be turned in in-class. Assignments must be typeset in Latex. Answer
Homework 5
CS 155 Spring 2013
March 15, 2013
Problem 1
(4.18)
have
Dene the random variables Xi = pi bi (t), 1 i n, and let X =
n
i=1 Xi .
We
1
E etXi = (etpi + etpi ).
2
x we have (using the same arg
Problem 2.32
Part a
Let Ei be the event that the ith candidate is the best and he is hired.
P r(Ei ) = P r(candidate Ei is chosen|Ei is the best) P r(Ei is the best)
1
n
P r(candidate Ei is chosen|Ei
CS155 - Homework 1
Justin Oh(sjo)
Homework 1
Problem 1
(a) The pooled sample of k people will be positive if at least one of the k individuals is positive.
The probability that none of individuals are
CS155
Probabilistic Methods in CS
Upfal
Homework 5
Due: Thu 5 March 2015, 2:30pm
Assignments will be handed in class. Assignments must be typeset in Latex.
Answers must be concise and correct. No late
CS155 - Homework 1
Lorenzo De Stefani(lorenzo)
Homework 1
Problem 1
(a) The probability that exactly k ips occur in traversing the n relays is given by:
n k
p (1 p)nk ,
k
(1)
for i = 0, 1, 2, . . . ,
CS155: Probability and Computing:
Randomized Algorithms and Probabilistic
Analysis
Eli Upfal
Eli [email protected]
Office: 319
TAs: Ahmad Mahmoody
and
Shashwat Silas
[email protected]
It is remarkab
CS155 - Homework 3
()
Homework 3
Problem 1
(a) Note rst that:
t
t
E[(1/t)
t
Xi ] = (1/t)
i=1
E[Xi ] = (1/t)
i=1
E[X] = E[X]
i=1
and since the Xi s are independent:
t
t
Xi ) = (1/t)2 V (
V (1/t)
i=1
t
The Probabilistic Method
Compute
n
i
i=0
n
i
1
2
n
The Probabilistic Method
Compute
n
n
i
i
i=0
n
1
2
Let X B(n.1/2),
n
E [X ] =
i
i=0
n
i
1
2
n
=
n
2
We prove a deterministic statement using a pr
Random Variable
Denition
A random variable X on a sample space is a real-valued
function on ; that is, X : R. A discrete random variable is
a random variable that takes on only a nite or countably inn
CS155 - Homework 4
solution (solution)
Homework 4
Problem 1
(a) By tessellating the original square S we obtain n/ (b log n) sub-squares sj , with j cfw_1, 2, . . . , n/b log n
each of size b log n. L
CS155
Probabilistic Methods in CS
Upfal
Homework 6
Due: Thu 12 March 2015, 2:30pm
Assignments will be handed in class. Assignments must be typeset in Latex.
Answers must be concise and correct. No lat
CS155
Probabilistic Methods in CS
Upfal
Homework 3
Due: Thu 19 Feb 2015, 2:30pm
Assignments will be handed in class. Assignments must be typeset in Latex.
Answers must be concise and correct. No late
CSCI 1550
Randomized Algorithms and Probabilistic Analysis
1
Prof. Eli Upfal
Homework 1
DUE: 2/5/2015
Please Note:
Assignments will be handed in class. Assignments must be typeset in Latex. Answers mu
CS155
Probabilistic Methods in CS
Upfal
Homework 4
Due: Thu 26 Feb 2015, 2:30pm
Assignments will be handed in class. Assignments must be typeset in Latex.
Answers must be concise and correct. No late
CS155 - Homework 2
()
Homework 2
Problem 1
Let Yi be the result of the i-th spin. Since the probability of winning in a certain round is 1 , we
2
1
know that P r(Yi = 1) = 1 and P r(Yi = 0) = 2 . Let