Probstat/birthday practice - ประวัติรุ่นแก้ไข

Jittat เมื่อ 06:23, 25 กันยายน 2557

2014-09-25T06:23:48Z

Jittat เมื่อ 06:23, 25 กันยายน 2557

2014-09-25T06:23:16Z

Jittat เมื่อ 03:19, 25 กันยายน 2557

2014-09-25T03:19:02Z

Jittat เมื่อ 03:18, 25 กันยายน 2557

2014-09-25T03:18:23Z

Jittat เมื่อ 03:14, 25 กันยายน 2557

2014-09-25T03:14:51Z

Jittat เมื่อ 02:44, 25 กันยายน 2557

2014-09-25T02:44:12Z

Jittat: หน้าที่ถูกสร้างด้วย ': ''This is part of probstat''. '''Please watch the clips ( [http://www.youtube.com/watch?v=TcAbDItb2RM part 1], [http://www.youtu...'

2014-09-25T02:39:20Z

หน้าที่ถูกสร้างด้วย ': ''This is part of probstat''. '''Please watch the clips ( [http://www.youtube.com/watch?v=TcAbDItb2RM part 1], [http://www.youtu...'

หน้าใหม่

: ''This is part of [[probstat]]''.

'''Please watch the clips ( [http://www.youtube.com/watch?v=TcAbDItb2RM part 1], [http://www.youtube.com/watch?v=E9-lt3r2oJY part 2] ) first, and think about how to use the balls-and-bins experiment to analyze the birthday problem before you continue.'''

@@ แถว 1: / แถว 1: @@
 : ''This is part of [[probstat]] and [[Probstat/week6 practice 2]].''
-{{กล่องเทา|'''Please watch the clips ([http://www.youtube.com/watch?v=TcAbDItb2RM part 1], [http://www.youtube.com/watch?v=E9-lt3r2oJY part 2]) first, and think about how to use the balls-and-bins experiment to analyze the birthday problem before you continue.'''}}
+: '''Please watch the clips ([http://www.youtube.com/watch?v=TcAbDItb2RM part 1], [http://www.youtube.com/watch?v=E9-lt3r2oJY part 2]) first, and think about how to use the balls-and-bins experiment to analyze the birthday problem before you continue.'''
 We shall indirectly analyze the birthday problem.  Instead of thinking about the event that some pair of balls lands into the same bin, we shall try to count the expected number of pairs of balls that land into the same bin.  (Can you imagine why this is our choice?  What is hard about thinking the former approach?)

@@ แถว 1: / แถว 1: @@
 : ''This is part of [[probstat]] and [[Probstat/week6 practice 2]].''
-'''Please watch the clips ([http://www.youtube.com/watch?v=TcAbDItb2RM part 1], [http://www.youtube.com/watch?v=E9-lt3r2oJY part 2]) first, and think about how to use the balls-and-bins experiment to analyze the birthday problem before you continue.'''
+{{กล่องเทา|'''Please watch the clips ([http://www.youtube.com/watch?v=TcAbDItb2RM part 1], [http://www.youtube.com/watch?v=E9-lt3r2oJY part 2]) first, and think about how to use the balls-and-bins experiment to analyze the birthday problem before you continue.'''}}
 We shall indirectly analyze the birthday problem.  Instead of thinking about the event that some pair of balls lands into the same bin, we shall try to count the expected number of pairs of balls that land into the same bin.  (Can you imagine why this is our choice?  What is hard about thinking the former approach?)

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 03:19, 25 กันยายน 2557
แถว 1:		แถว 1:
−	: ''This is part of [[probstat]]''.	+	: ''This is part of [[probstat]] and [[Probstat/week6 practice 2]].''

	'''Please watch the clips ([http://www.youtube.com/watch?v=TcAbDItb2RM part 1], [http://www.youtube.com/watch?v=E9-lt3r2oJY part 2]) first, and think about how to use the balls-and-bins experiment to analyze the birthday problem before you continue.'''		'''Please watch the clips ([http://www.youtube.com/watch?v=TcAbDItb2RM part 1], [http://www.youtube.com/watch?v=E9-lt3r2oJY part 2]) first, and think about how to use the balls-and-bins experiment to analyze the birthday problem before you continue.'''

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 03:18, 25 กันยายน 2557
แถว 21:		แถว 21:
	Hint: Maybe this definition is useful: For each pair of different balls ''i'' and ''j'', let random variable <math>X_{ij}</math> be 1 if ball ''i'' and ball ''j'' land into the same bin.		Hint: Maybe this definition is useful: For each pair of different balls ''i'' and ''j'', let random variable <math>X_{ij}</math> be 1 if ball ''i'' and ball ''j'' land into the same bin.

−	2.	+	2. Find the minimum value of ''k'' as a function of ''n'' such that '''E[X] = 1'''. (This is the number of balls such that we expect to see one collision.)
		+
		+	3. Let ''n'' = 365, use your answer in 2, to find ''k''. Compare this value to 23.
		+
		+	4. If we want no two balls to land in the same bin, can we use this analysis to give you a hint on the upperbound on ''k''?

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 03:14, 25 กันยายน 2557
แถว 2:		แถว 2:

	'''Please watch the clips ([http://www.youtube.com/watch?v=TcAbDItb2RM part 1], [http://www.youtube.com/watch?v=E9-lt3r2oJY part 2]) first, and think about how to use the balls-and-bins experiment to analyze the birthday problem before you continue.'''		'''Please watch the clips ([http://www.youtube.com/watch?v=TcAbDItb2RM part 1], [http://www.youtube.com/watch?v=E9-lt3r2oJY part 2]) first, and think about how to use the balls-and-bins experiment to analyze the birthday problem before you continue.'''
		+
		+	We shall indirectly analyze the birthday problem. Instead of thinking about the event that some pair of balls lands into the same bin, we shall try to count the expected number of pairs of balls that land into the same bin. (Can you imagine why this is our choice? What is hard about thinking the former approach?)
		+
		+	To illustrate what we are trying to count, let's consider the sample outcome of throwing 6 balls into 3 bins:
		+
		+	bin 1: 1, 3
		+	bin 2: 4, 5, 6
		+	bin 3: 2
		+
		+	In this sample, there are 4 pairs of balls that land into the same bin: (1-3), (4-5), (5-6), and (4-6).
		+
		+	Let's define our experiment: We throw ''k'' balls into ''n'' bins uniformly independently at random.
		+
		+	Let random variable ''X'' be the number of pairs of balls that fall into the same bin.
		+
		+	1. Find '''E[X]'''.
		+
		+	Hint: Maybe this definition is useful: For each pair of different balls ''i'' and ''j'', let random variable <math>X_{ij}</math> be 1 if ball ''i'' and ball ''j'' land into the same bin.
		+
		+	2.

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 02:44, 25 กันยายน 2557
แถว 1:		แถว 1:
	: ''This is part of [[probstat]]''.		: ''This is part of [[probstat]]''.

−	'''Please watch the clips ( [http://www.youtube.com/watch?v=TcAbDItb2RM part 1], [http://www.youtube.com/watch?v=E9-lt3r2oJY part 2] ) first, and think about how to use the balls-and-bins experiment to analyze the birthday problem before you continue.'''	+	'''Please watch the clips ([http://www.youtube.com/watch?v=TcAbDItb2RM part 1], [http://www.youtube.com/watch?v=E9-lt3r2oJY part 2]) first, and think about how to use the balls-and-bins experiment to analyze the birthday problem before you continue.'''