Probstat/coupon practice - ประวัติรุ่นแก้ไข

Jittat: /* Computing the expectation */

2014-09-25T06:51:08Z

Computing the expectation

Jittat: /* Computing the expectation */

2014-09-25T06:50:52Z

Computing the expectation

Jittat: /* Analysis on the probability */

2014-09-25T06:46:36Z

Analysis on the probability

Jittat เมื่อ 06:24, 25 กันยายน 2557

2014-09-25T06:24:19Z

Jittat: หน้าที่ถูกสร้างด้วย ': ''This is part of probstat and Probstat/week6 practice 2.'' '''Please watch the 1st clip ([http://www.youtube.com/watch?v=Tc...'

2014-09-25T06:22:55Z

หน้าที่ถูกสร้างด้วย ': ''This is part of probstat and Probstat/week6 practice 2.'' '''Please watch the 1st clip ([http://www.youtube.com/watch?v=Tc...'

หน้าใหม่

: ''This is part of [[probstat]] and [[Probstat/week6 practice 2]].''

'''Please watch the 1st clip ([http://www.youtube.com/watch?v=TcAbDItb2RM part 1]), and think about how to use the balls-and-bins experiment to analyze the coupon collector's problem before watching the 2nd clip ([http://www.youtube.com/watch?v=E9-lt3r2oJY part 2]). If you have tried to use the approach we used to analyze the fullest bin to find the upperbound for the number balls, please proceed on this page.'''

@@ แถว 9: / แถว 9: @@
 == Computing the expectation ==
-: Please watch the 2nd clip on the coupon collector's problem before attempting this section.
+: ''Please watch the 2nd clip on the coupon collector's problem before attempting this section.''
 Consider the following experiment: we throw a ball randomly into ''n'' bins.  We keep throwing a ball until there is no empty bins.

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 06:50, 25 กันยายน 2557
แถว 9:		แถว 9:

	== Computing the expectation ==		== Computing the expectation ==
		+	: Please watch the 2nd clip on the coupon collector's problem before attempting this section.
		+
		+	Consider the following experiment: we throw a ball randomly into ''n'' bins. We keep throwing a ball until there is no empty bins.
		+
		+	Let random variable ''X'' denote the number of balls that we throw.
		+
		+	Find '''E[X]'''.
		+
		+	'''Hint questions:'''
		+	* Suppose that we have already got n-1 different coupons.
		+	** What's the probability that we get the last coupon when we buy a new box of candies?
		+	** Suppose that you have got n-1 different coupons. What is the expected number of boxes that we have to buy to get the last coupon?
		+	* Suppose that we have already got n-2 different coupons.
		+	** What's the probability that we get the (n-1)-th new coupon after buying one box of candies?
		+	** Suppose that you have got n-1 different coupons. What is the expected number of boxes that we have to buy to get the (n-1)-th new coupon?

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 06:46, 25 กันยายน 2557
แถว 4:		แถว 4:

	== Analysis on the probability ==		== Analysis on the probability ==
		+	Use the approach that we analyze the fullest bin to find the upper bound on the probability that we throw ''k'' balls into ''n'' bin and there exists some bin which is empty.
		+
		+	'''Hint:''' Try define an appropriate event ''B<sub>i</sub>'' for bin ''i''.

	== Computing the expectation ==		== Computing the expectation ==

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 06:24, 25 กันยายน 2557
แถว 1:		แถว 1:
	: ''This is part of [[probstat]] and [[Probstat/week6 practice 2]].''		: ''This is part of [[probstat]] and [[Probstat/week6 practice 2]].''

−	'''Please watch the 1st clip ([http://www.youtube.com/watch?v=TcAbDItb2RM part 1]), and think about how to use the balls-and-bins experiment to analyze the coupon collector's problem before watching the 2nd clip ([http://www.youtube.com/watch?v=E9-lt3r2oJY part 2]). If you have tried to use the approach we used to analyze the fullest bin to find the upperbound for the number balls, please proceed on this page.'''	+	: '''Please watch the 1st clip ([http://www.youtube.com/watch?v=TcAbDItb2RM part 1]), and think about how to use the balls-and-bins experiment to analyze the coupon collector's problem before watching the 2nd clip ([http://www.youtube.com/watch?v=E9-lt3r2oJY part 2]). If you have tried to use the approach we used to analyze the fullest bin to find the upperbound for the number balls, please proceed on this page.'''
		+
		+	== Analysis on the probability ==
		+
		+	== Computing the expectation ==