Difference between revisions of "Homework8 ECE302Fall2008sanghavi" - Rhea

Latest revision as of 12:58, 22 November 2011

Instructions

Homework 8 can be downloaded here on the ECE 302 course website.

Problem 1: Gone Fishin'

On average, it takes 1 hour to catch a fish.

(a) What is (an upper bound on) the probability that it will take 3 hours?
(b) Landis only has 2 hours to spend fishing. What is (an upper bound on) the probability he will go home fish-less?

Problem 2: Bounded Variance

(a) What is the maximum variance possible for a Bernoulli random variable?
(b) What is the maximum variance possible for a binomial random variable, with parameter $$ n = 1000 $$ ?
(c) If $$ X $$ is uniform on $$ [a,b] $$ , what is its variance?
Problem 2a - Beau Morrison_ECE302Fall2008sanghavi
Katie Pekkarinen 8.2b_ECE302Fall2008sanghavi
2-c Seraj Dosenbach_ECE302Fall2008sanghavi
Divyanshu Kamboj - 2.a_ECE302Fall2008sanghavi
Shao-Fu Shih - 2.c_ECE302Fall2008sanghavi
Anand Gautam -2.a_ECE302Fall2008sanghavi
Ken Pesyna -2.a,b_ECE302Fall2008sanghavi

Problem 3: "Bias" Estimate

(a) You have a coin of unknown bias. You flip it 10 times, and get TTHHTHTTHT as the sequence of outcomes. What is the maximum likelihood estimate of the bias (i.e. the probability, $$ p $$ , of heads)?
(b) A friend has a coin of unknown bias. He flips it $$ n $$ times, and finds that $$ k $$ of them were heads. However, he neglects to record the exact sequence. What is the max-likelihood estimate for the bias in this case?

Problem 4: Votes are In

The election is over and the votes have been cast. If all the votes were counted, it would show that McCain has won Tippecanoe county. However, the Tippecanoe election officer is lazy however, and decides he is just going to count 1000 random votes. He does so, and finds 600 for Obama and 400 for McCain. He declares Obama has won Tippecanoe. What is (an upper bound on) such an event occuring? (Assume, as in class, that Tippecanoe has an infinite number of people.)

Hint: Let $$ p $$ be the true fraction of people that voted for Obama. We know that $$ p < 1/2 $$ . Now find and upper bound on the event as a function of $$ p $$ , and then maximize over $$ p $$ .

Back to ECE302 Fall 2008 Prof. Sanghavi

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+[[Category:ECE302Fall2008_ProfSanghavi]]
+[[Category:probabilities]]
+[[Category:ECE302]]
+[[Category:homework]]
+[[Category:problem solving]]
 == Instructions ==
 Homework 8 can be [https://engineering.purdue.edu/ece302/homeworks/HW8FA08.pdf downloaded here] on the [https://engineering.purdue.edu/ece302/ ECE 302 course website].
@@ Line 6: / Line 12: @@
 *(a) What is (an upper bound on) the probability that it will take 3 hours?
 *(b) Landis only has 2 hours to spend fishing. What is (an upper bound on) the probability he will go home fish-less?
+*[[Gregory Pajot 8.1a_ECE302Fall2008sanghavi]]
+*[[Christopher Wacnik 8.1a_ECE302Fall2008sanghavi]]
+*[[Ben Carter 8.1b_ECE302Fall2008sanghavi]]
+*[[Zhongtian Wang 8.1_ECE302Fall2008sanghavi]]
+*[[Tiffany Sukwanto 8.1_ECE302Fall2008sanghavi]]
+*[[Chris Rush 8.1b_ECE302Fall2008sanghavi]]
+*[[Nicholas BRowdues_ECE302Fall2008sanghavi]]
 == Problem 2: Bounded Variance ==
@@ Line 11: / Line 25: @@
 *(b) What is the maximum variance possible for a binomial random variable, with parameter <math>n = 1000</math>?
 *(c) If <math>X</math> is uniform on <math>[a,b]</math>, what is its variance?
+*[[Problem 2a - Beau Morrison_ECE302Fall2008sanghavi]]
+*[[Katie Pekkarinen 8.2b_ECE302Fall2008sanghavi]]
+*[[2-c Seraj Dosenbach_ECE302Fall2008sanghavi]]
+*[[ Divyanshu Kamboj - 2.a_ECE302Fall2008sanghavi]]
+*[[ Shao-Fu Shih - 2.c_ECE302Fall2008sanghavi]]
+*[[Anand Gautam -2.a_ECE302Fall2008sanghavi]]
+*[[Ken Pesyna -2.a,b_ECE302Fall2008sanghavi]]
 == Problem 3: "Bias" Estimate ==
 *(a) You have a coin of unknown bias. You flip it 10 times, and get TTHHTHTTHT as the sequence of outcomes. What is the maximum likelihood estimate of the bias (i.e. the probability, <math>p</math>, of heads)?
 *(b) A friend has a coin of unknown bias. He flips it <math>n</math> times, and finds that <math>k</math> of them were heads. However, he neglects to record the exact sequence. What is the max-likelihood estimate for the bias in this case?
+*[[Hamad Al Shehhi 8.3.a,b_ECE302Fall2008sanghavi]]
+*[[Joon Young Kim 8.3.a_ECE302Fall2008sanghavi]]
+*[[Zhongtian Wang easier way for finding P_ECE302Fall2008sanghavi]]
+*[[Michael Allen 8.3.a_ECE302Fall2008sanghavi]]
+*[[Arie Lyles 8.3.a_ECE302Fall2008sanghavi]]
+*[[Patrick M. Avery Jr. 8.3a & b_ECE302Fall2008sanghavi]]
+*[[Joshua Long 8.3_ECE302Fall2008sanghavi]]
+*[[Jaewoo choi 8.3_ECE302Fall2008sanghavi]]
 == Problem 4: Votes are In ==
-The election is over and the votes have been cast. The Tippecanoe election officer is lazy however, and decides he is just going to see a 1000 random votes. He does so, and finds 600 for Obama and 400 for McCain.  He declares Obama has won Tippecanoe. What is (an upper bound on) the probability that he is wrong?  (Assume, as in class, that Tippecanoe has infinite people.)
+The election is over and the votes have been cast. If all the votes were counted, it would show that McCain has won Tippecanoe county. However, the Tippecanoe election officer is lazy however, and decides he is just going to count 1000 random votes. He does so, and finds 600 for Obama and 400 for McCain. He declares Obama has won Tippecanoe. What is (an upper bound on) such an event occuring? (Assume, as in class, that Tippecanoe has an infinite number of people.)
+Hint: Let <math>p</math> be the true fraction of people that voted for Obama. We know that <math>p < 1/2</math>. Now find and upper bound on the event as a function of <math>p</math>, and then maximize over <math>p</math>.
+*[[Andrew Hermann 8.4_ECE302Fall2008sanghavi]]
+*[[Junzhe Geng 8.4_ECE302Fall2008sanghavi]]
+*[[Brian Thomas 8.4_ECE302Fall2008sanghavi]]
+*[[Spencer Mitchell 8.4_ECE302Fall2008sanghavi]]
+*[[Justin Mauck 8.4_ECE302Fall2008sanghavi]]
+----
+[[Main_Page_ECE302Fall2008sanghavi|Back to ECE302 Fall 2008 Prof. Sanghavi]]