Probstat/homework 3 - ประวัติรุ่นแก้ไข

Jittat: /* Part 2: Hypothesis testing */

2014-12-09T02:39:31Z

Part 2: Hypothesis testing

Jittat: /* Part 2: Hypothesis testing */

2014-12-09T02:39:12Z

Part 2: Hypothesis testing

Jittat: /* Part 3: Regression */

2014-12-09T02:36:26Z

Part 3: Regression

Jittat: /* Part 3: Regression */

2014-12-09T02:36:17Z

Part 3: Regression

Jittat: /* Part 3: Regression */

2014-12-09T02:28:31Z

Part 3: Regression

Jittat: /* Part 1: Poisson and exponential random variables */

2014-12-09T02:18:57Z

Part 1: Poisson and exponential random variables

Jittat: /* Part 1: Poisson and exponential random variables */

2014-12-09T02:15:10Z

Part 1: Poisson and exponential random variables

Jittat: /* Part 2: Hypothesis testing */

2014-12-09T02:05:34Z

Part 2: Hypothesis testing

Jittat: /* Part 2: Hypothesis testing */

2014-12-09T01:30:48Z

Part 2: Hypothesis testing

Jittat: /* Part 3: Regression */

2014-12-09T01:16:13Z

Part 3: Regression

@@ แถว 19: / แถว 19: @@
 . We want to test if students who have breakfast perform better in the exam than students who do not.  From the data we collect over time, we believe that test scores are normally distributed and the variance of the test score is 120.  We sample 30 students from the first group and 30 students from the second group, and collect their test scores.  Describe a null hypothesis and show how to perform a hypothesis testing for this problem.  Describe the criteria with 5% level of significance.
-. The time it takes for a web server to crash (in hours) is exponentially distributed.   The company that builds the server claims that the server has an average up time of <math>h</math> hours.  We collect a sample of its up times <math>X_1,X_2,\ldots,X_20</math>.  Describe a hypothesis testing procedure with %5 level of significance that the average up time is at least <math>h</math> hours.
+. The time it takes for a web server to crash (in hours) is exponentially distributed.   The company that builds the server claims that the server has an average up time of <math>h</math> hours.  We collect a sample of its up times <math>X_1,X_2,\ldots,X_{20}</math>.  Describe a hypothesis testing procedure with %5 level of significance that the average up time is at least <math>h</math> hours as claimed by the company.
 == Part 3: Regression ==

@@ แถว 19: / แถว 19: @@
 . We want to test if students who have breakfast perform better in the exam than students who do not.  From the data we collect over time, we believe that test scores are normally distributed and the variance of the test score is 120.  We sample 30 students from the first group and 30 students from the second group, and collect their test scores.  Describe a null hypothesis and show how to perform a hypothesis testing for this problem.  Describe the criteria with 5% level of significance.
-.
+. The time it takes for a web server to crash (in hours) is exponentially distributed.   The company that builds the server claims that the server has an average up time of <math>h</math> hours.  We collect a sample of its up times <math>X_1,X_2,\ldots,X_20</math>.  Describe a hypothesis testing procedure with %5 level of significance that the average up time is at least <math>h</math> hours.
 == Part 3: Regression ==

@@ แถว 40: / แถว 40: @@
 . (IPSES, problem 21, chapter 7.) Consider a different regression model where
-<center><math>Y = \betaX + e,</math></center>
+<center><math>Y = \beta X + e,</math></center>
 where <math>e\sim Normal(0,\sigma^2)</math>.
 Suppose that we get a sample <math>(x_1,y_1),\ldots,(x_n,y_n)</math>.  Find the least square estimator <math>B</math> for <math>\beta</math>.

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 02:36, 9 ธันวาคม 2557
แถว 38:		แถว 38:
	* Estimate the variance <math>\sigma^2</math> of the error.		* Estimate the variance <math>\sigma^2</math> of the error.

−	2.	+	2. (IPSES, problem 21, chapter 7.) Consider a different regression model where
		+
		+	<center><math>Y = \betaX + e,</math></center>
		+
		+	where <math>e\sim Normal(0,\sigma^2)</math>.
		+
		+	Suppose that we get a sample <math>(x_1,y_1),\ldots,(x_n,y_n)</math>. Find the least square estimator <math>B</math> for <math>\beta</math>.

@@ แถว 22: / แถว 22: @@
 == Part 3: Regression ==
-.
+. Consider the following data:
 .

@@ แถว 8: / แถว 8: @@
 . The time it takes for a web server to crash (in hours) is exponentially distributed with parameter <math>\lambda = 0.001</math>.  What is the probability that the web server crashes within 2 weeks (14 days) of operation?
-.
+. A system consists of 5 components.  It will fail if any of its components are broken.  The lifetime of each component <math>i</math> (in minutes) is exponentially distributed with parameter <math>\lambda_i</math>.   What is the probability that the system works for <math>t</math> minutes?
 == Part 2: Hypothesis testing ==

@@ แถว 6: / แถว 6: @@
 . On average, each day Programmer Lazy puts in 5 bugs to the code.  The manager tries to give incentives for the programmer to improve, so the manager decides to give a reward to the programmer on any day Programmer Lazy only puts in ''less than'' 3 bugs.  If the number of bugs is a Poisson distributed random variable and Programmer Lazy does not change at all, what is the probability that Programmer Lazy gets a reward on any day?
-.
+. The time it takes for a web server to crash (in hours) is exponentially distributed with parameter <math>\lambda = 0.001</math>.  What is the probability that the web server crashes within 2 weeks (14 days) of operation?
 .

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 02:05, 9 ธันวาคม 2557
แถว 18:		แถว 18:

	4. We want to test if students who have breakfast perform better in the exam than students who do not. From the data we collect over time, we believe that test scores are normally distributed and the variance of the test score is 120. We sample 30 students from the first group and 30 students from the second group, and collect their test scores. Describe a null hypothesis and show how to perform a hypothesis testing for this problem. Describe the criteria with 5% level of significance.		4. We want to test if students who have breakfast perform better in the exam than students who do not. From the data we collect over time, we believe that test scores are normally distributed and the variance of the test score is 120. We sample 30 students from the first group and 30 students from the second group, and collect their test scores. Describe a null hypothesis and show how to perform a hypothesis testing for this problem. Describe the criteria with 5% level of significance.
		+
		+	5.

	== Part 3: Regression ==		== Part 3: Regression ==

@@ แถว 17: / แถว 17: @@
 . We are interested in testing if a normally-distributed population has mean at least 100.  However, we do not know the population variance.  If we decide to take a sample of size 10 to compute the sample mean <math>\bar{X}</math> and the sample variance <math>S^2</math>, design a hypothesis testing procedure with the level of significance <math>\alpha=10%</math>.  State the null hypothesis clearly and describe the criteria for accepting/rejecting the null hypothesis.
-. We want to test if students who have breakfast perform better in the exam than students who do not.  From the data we collect over time, we believe that the variance of the test score is 120.  We sample 30 students from the first group and 30 students from the second group, and collect their test scores.  Describe a null hypothesis and show how to perform a hypothesis testing for this problem.  Describe the criteria with 5% level of significance.
+. We want to test if students who have breakfast perform better in the exam than students who do not.  From the data we collect over time, we believe that test scores are normally distributed and the variance of the test score is 120.  We sample 30 students from the first group and 30 students from the second group, and collect their test scores.  Describe a null hypothesis and show how to perform a hypothesis testing for this problem.  Describe the criteria with 5% level of significance.
 == Part 3: Regression ==

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 01:16, 9 ธันวาคม 2557
แถว 20:		แถว 20:

	== Part 3: Regression ==		== Part 3: Regression ==
		+	1.
		+
		+	2.