Probstat/week4 practice 1 - ประวัติรุ่นแก้ไข

Jittat: /* No one gets her/his own hat back */

2014-09-18T07:30:07Z

No one gets her/his own hat back

2014-09-18T07:28:30Z

= No empty bins

2014-09-18T07:27:21Z

No one gets her/his own hat back

2014-09-11T03:47:34Z

Practice problems

2014-09-09T03:29:00Z

Practice problems

2014-09-09T02:51:25Z

Practice problems

2014-09-09T02:37:28Z

2014-09-09T02:32:06Z

Practice problems

2014-09-09T02:31:44Z

Practice problems

2014-09-09T02:25:56Z

Practice problems

@@ แถว 37: / แถว 37: @@
 === <del>No one gets her/his own hat back</del> ===
-: '''Notes:''' This question is wrong... sorry please ignore it.
+: '''''Notes:''' I am sorry this question is wrong... please ignore it.''
 == No empty bins:  Sterling's approximation ==

@@ แถว 39: / แถว 39: @@
 : '''Notes:''' This question is wrong... sorry please ignore it.
-=== No empty bins ==
+== No empty bins:  Sterling's approximation ==
-Let's try to approximate the probability that no one gets her/his own hat back in the random hat experiment.
+Let's reconsider the balls-and-bins experiment and try to approximate the probability that there is no empty bins.
-. In the random hat experiment what is the probability that no one get her/his own hat back?  Give the exact answer.
+. What is the probability that there is no empty bin?
 This is the Sterling's approximation of factorial (See [http://en.wikipedia.org/wiki/Stirling%27s_approximation wikipedia entry])

@@ แถว 35: / แถว 35: @@
 . Let '''n''' = 500.  Write a program that estimates the probability that '''X''' is greater than 0.  Plot the probability distribution of '''X'''.
-=== No one gets her/his own hat back ===
+=== <del>No one gets her/his own hat back</del> ===
 Let's try to approximate the probability that no one gets her/his own hat back in the random hat experiment.

@@ แถว 7: / แถว 7: @@
 . We toss a fair coin many times until we get a Head.  Let random variable '''X''' be the number of times we have to toss the coin.  For a non-negative integer '''i''', find '''P{X > i}'''.  (You should leave '''i''' as a variable in your answer.)
-. We toss a coin that turns up head with probability '''p'''.  Also, let '''q = 1 - p'''.  Let random variable '''X''' be the number of times we have to toss the coin.  For a non-negative integer '''i''', find '''P{X > i}'''.
+. Under the same condition as in question 3, but we toss a coin that turns up head with probability '''p'''.  Also, let '''q = 1 - p'''.  Let random variable '''X''' be the number of times we have to toss the coin.  For a non-negative integer '''i''', find '''P{X > i}'''.
 == Two experiments ==

@@ แถว 5: / แถว 5: @@
 . In roulette, there are 38 pockets on the roulette wheel.  The pockets are numbered 0,00,1,2,3,...,36.  If you bet 1 baht on 00 and win, you will get 35 baht (not including your 1-baht bet).  If you bet 1 baht on 00, what is the expected value of money that you get in return?
-. We toss a fair coin many times until we get a Head.  Let random variable '''X''' be the number of times we have to toss the coin.  Find '''P{X > i}'''.
+. We toss a fair coin many times until we get a Head.  Let random variable '''X''' be the number of times we have to toss the coin.  For a non-negative integer '''i''', find '''P{X > i}'''.  (You should leave '''i''' as a variable in your answer.)
-. We toss a coin that turns up head with probability '''p'''.  Also, let '''q = 1 - p'''.  Let random variable '''X''' be the number of times we have to toss the coin.  Find '''P{X > i}'''.
+. We toss a coin that turns up head with probability '''p'''.  Also, let '''q = 1 - p'''.  Let random variable '''X''' be the number of times we have to toss the coin.  For a non-negative integer '''i''', find '''P{X > i}'''.
 == Two experiments ==

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 02:37, 9 กันยายน 2557
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		+	: ''This is part of [[probstat]]''.
	== Practice problems ==		== Practice problems ==
	1. We toss a fair dice 2 times. Let random variable '''X''' be the product of the values from the dices. Plot the pmf of '''X'''.		1. We toss a fair dice 2 times. Let random variable '''X''' be the product of the values from the dices. Plot the pmf of '''X'''.

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 02:31, 9 กันยายน 2557
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	2. We toss a coin that turns up head with probability '''p'''. Also, let '''q = 1 - p'''. Let random variable '''X''' be the number of times we have to toss the coin. Find '''P{X > i}'''.		2. We toss a coin that turns up head with probability '''p'''. Also, let '''q = 1 - p'''. Let random variable '''X''' be the number of times we have to toss the coin. Find '''P{X > i}'''.
		+
		+	3. We toss a fair dice 2 times. Let random variable '''X''' be the product of the values from the dices. Plot the pmf of '''X'''.

	== Two experiments ==		== Two experiments ==

@@ แถว 1: / แถว 1: @@
 == Practice problems ==
 == Two experiments ==
 In this section, we shall analyze two experiments.