Probstat/week5 practice 2 - ประวัติรุ่นแก้ไข

Jittat: /* Independent trials */

2014-09-17T17:30:34Z

Independent trials

2014-09-17T17:30:10Z

Independent trials

2014-09-17T17:27:06Z

Independent trials

2014-09-17T17:25:47Z

Independent trials

2014-09-17T17:25:03Z

Independent random variables

2014-09-17T17:21:20Z

Independent random variables

2014-09-17T17:13:23Z

Independent random variables

2014-09-17T17:10:00Z

Independent random variables

2014-09-17T17:07:01Z

2014-09-17T16:48:52Z

หน้าที่ถูกสร้างด้วย ': ''This is part of probstat.'''

หน้าใหม่

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

@@ แถว 2: / แถว 2: @@
 == Independent trials ==
-. There is an electric calculation circuit that, given the input, it gives the wrong answer with probability 0.1.  What is the probability that we use the circuit for 10 times and always get the correct answer.
+. There is an electric calculation circuit that, given the input, it gives the wrong answer with probability 0.1.  What is the probability that we use the circuit for 10 times and always get the correct answers.
 . There is a random experiment whose outcomes are successful with probability 1/2.  We would like to perform the experiment for ''K'' times.  What is the probability that none of the outcomes from these ''K'' experiments is successful.  What is the minimum value of ''K'' if we want the probability to be less than 1/''n''<sup>2</sup>, for some value ''n''.

@@ แถว 2: / แถว 2: @@
 == Independent trials ==
-. There is a random experiment whose outcomes are successful with probability 1/2.  We would like to perform the experiment for ''K'' times.  What is the probability that none of the outcomes from these ''K'' experiments is successful.  What is the minimum value of ''K'' if we want the probability to be less than 1/''n''<sup>2</sup>, for some value ''n''.
+. There is an electric calculation circuit that, given the input, it gives the wrong answer with probability 0.1.  What is the probability that we use the circuit for 10 times and always get the correct answer.
 Note: the minimum value of ''K'' should be a function of the value of ''n''.

@@ แถว 3: / แถว 3: @@
 == Independent trials ==
 . There is a random experiment whose outcomes are successful with probability 1/2.  We would like to perform the experiment for ''K'' times.  What is the probability that none of the outcomes from these ''K'' experiments is successful.  What is the minimum value of ''K'' if we want the probability to be less than 1/''n''<sup>2</sup>, for some value ''n''.
 == Independent random variables ==

@@ แถว 2: / แถว 2: @@
 == Independent trials ==
-. There is a random experiment whose outcomes are successful with probability 1/2.  We would like to perform the experiment for ''K'' times.  What is the probability that none of the outcomes from these ''K'' experiments is successful.  What is the minimum value of ''K'' if we want the probability to be less than 1/''n''.
+. There is a random experiment whose outcomes are successful with probability 1/2.  We would like to perform the experiment for ''K'' times.  What is the probability that none of the outcomes from these ''K'' experiments is successful.  What is the minimum value of ''K'' if we want the probability to be less than 1/''n''<sup>2</sup>, for some value ''n''.
 == Independent random variables ==

@@ แถว 1: / แถว 1: @@
 : ''This is part of [[probstat]].''
 == Independent random variables ==
+. Consider a simple random experiment of choosing, uniformly at random, an integer from the set {0,1}.
 * 1.1 Let ''X'' be a random variable that denotes the chosen integer from the experiment.  Find E[''X''] and ''Var(X)''.

@@ แถว 7: / แถว 7: @@
 * 1.1 Let ''X'' be a random variable that denotes the chosen integer from the experiment.  Find E[''X''] and ''Var(X)''.
 * 1.2 Let's perform the experiment 2 times.  Let ''X''<sub>1</sub> and ''X''<sub>2</sub> be random variables that denote the chosen integers from the first and the second experiments.  Let ''Y'' = (''X''<sub>1</sub> + ''X''<sub>2</sub>)/2.  Find E[''Y''] and ''Var(Y)''.
-* 1.2 Let's perform the experiment ''K'' times.  Let ''X''<sub>1</sub>, ''X''<sub>2</sub>,... ''X''<sub>K</sub>  be random variables that denote the chosen integers from each experiments.  Let ''Z'' = (''X''<sub>1</sub> + ... + ''X''<sub>K</sub>)/K.  Find E[''Z''] and ''Var(Z)''.
+* 1.3 Let's perform the experiment ''K'' times.  Let ''X''<sub>1</sub>, ''X''<sub>2</sub>,... ''X''<sub>K</sub>  be random variables that denote the chosen integers from each experiments.  Let ''Z'' = (''X''<sub>1</sub> + ... + ''X''<sub>K</sub>)/K.  Find E[''Z''] and ''Var(Z)''.

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 17:13, 17 กันยายน 2557
แถว 6:		แถว 6:

	* 1.1 Let ''X'' be a random variable that denotes the chosen integer from the experiment. Find E[''X''] and ''Var(X)''.		* 1.1 Let ''X'' be a random variable that denotes the chosen integer from the experiment. Find E[''X''] and ''Var(X)''.
−	* 1.2 Let's perform the experiment 2 times. Let ''X''<sub>1</sub> and ''X''<sub>2</sub> that denote the chosen integers from the first and the second experiments. Let ''Y'' = (''X''<sub>1</sub> + ''X''<sub>2</sub>)/2. Find E[''Y''] and ''Var(Y)''.	+	* 1.2 Let's perform the experiment 2 times. Let ''X''<sub>1</sub> and ''X''<sub>2</sub> be random variables that denote the chosen integers from the first and the second experiments. Let ''Y'' = (''X''<sub>1</sub> + ''X''<sub>2</sub>)/2. Find E[''Y''] and ''Var(Y)''.
		+	* 1.2 Let's perform the experiment ''K'' times. Let ''X''<sub>1</sub>, ''X''<sub>2</sub>,... ''X''<sub>K</sub> be random variables that denote the chosen integers from each experiments. Let ''Z'' = (''X''<sub>1</sub> + ... + ''X''<sub>K</sub>)/K. Find E[''Z''] and ''Var(Z)''.

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 17:10, 17 กันยายน 2557
แถว 6:		แถว 6:

	* 1.1 Let ''X'' be a random variable that denotes the chosen integer from the experiment. Find E[''X''] and ''Var(X)''.		* 1.1 Let ''X'' be a random variable that denotes the chosen integer from the experiment. Find E[''X''] and ''Var(X)''.
		+	* 1.2 Let's perform the experiment 2 times. Let ''X''<sub>1</sub> and ''X''<sub>2</sub> that denote the chosen integers from the first and the second experiments. Let ''Y'' = (''X''<sub>1</sub> + ''X''<sub>2</sub>)/2. Find E[''Y''] and ''Var(Y)''.

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 17:07, 17 กันยายน 2557
แถว 1:		แถว 1:
	: ''This is part of [[probstat]].''		: ''This is part of [[probstat]].''
		+
		+	== Independent random variables ==
		+
		+	1. Consider a simple experiment of choosing, uniformly at random, an integer from the set {0,1}.
		+
		+	* 1.1 Let ''X'' be a random variable that denotes the chosen integer from the experiment. Find E[''X''] and ''Var(X)''.