Probstat/week8 practice 2 - ประวัติรุ่นแก้ไข

Jittat: /* Challenging problems */

2014-10-09T03:14:54Z

Challenging problems

Jittat: /* Challenging problems */

2014-10-09T03:11:37Z

Challenging problems

Jittat: /* Basic practice */

2014-10-09T02:58:10Z

Basic practice

Jittat: /* Basic practice */

2014-10-09T02:55:51Z

Basic practice

Jittat: /* Basic practice */

2014-10-09T02:55:09Z

Basic practice

Jittat: /* Basic practice */

2014-10-09T02:52:30Z

Basic practice

Jittat: /* Basic practice */

2014-10-09T02:46:15Z

Basic practice

Jittat เมื่อ 02:45, 9 ตุลาคม 2557

2014-10-09T02:45:05Z

Jittat เมื่อ 02:43, 9 ตุลาคม 2557

2014-10-09T02:43:46Z

Jittat: หน้าที่ถูกสร้างด้วย ': ''This is part of probstat''. To compute the cdf of standard normal random variable, you can use a table from [http://en.wikiped...'

2014-10-09T02:41:45Z

หน้าที่ถูกสร้างด้วย ': ''This is part of probstat''. To compute the cdf of standard normal random variable, you can use a table from [http://en.wikiped...'

หน้าใหม่

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

To compute the cdf of standard normal random variable, you can use a table from [http://en.wikipedia.org/wiki/Standard_normal_table wikipedia].

@@ แถว 30: / แถว 30: @@
 . There are 2 types of fishes in the pond: type A and type B.  The average length of type-A fish is 50 cm with variance 10.  For type B, the average length is 65 cm with the same variance.  You want to classify these two types of fishes using just their lengths.
-* 1.1 Plot the density function of the lengths of fish of type A and of type B.  Plot them in the game graph (using different types of lines).
+* 1.1 Plot the density functions of the lengths of fish of type A and of type B.  Plot them in the same graph (using different types of lines).
 * 1.2 You want to classify the fishes using a single threshold '''L = 60'''.  That is, if you pick a random fish, and its length is at most '''L''', you will say that it is type A, and you will say that it is type B, otherwise.   What is the probability that the fish that you pick is actually of type A, but you classify it wrongly as type B.
 * 1.3 Using the threshold '''L = 60''', what is the probability that the fish that you pick is actually of type B, but you classify it wrongly as type A.

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 03:11, 9 ตุลาคม 2557
แถว 28:		แถว 28:

	== Challenging problems ==		== Challenging problems ==
		+	1. There are 2 types of fishes in the pond: type A and type B. The average length of type-A fish is 50 cm with variance 10. For type B, the average length is 65 cm with the same variance. You want to classify these two types of fishes using just their lengths.
		+
		+	* 1.1 Plot the density function of the lengths of fish of type A and of type B. Plot them in the game graph (using different types of lines).
		+	* 1.2 You want to classify the fishes using a single threshold '''L = 60'''. That is, if you pick a random fish, and its length is at most '''L''', you will say that it is type A, and you will say that it is type B, otherwise. What is the probability that the fish that you pick is actually of type A, but you classify it wrongly as type B.
		+	* 1.3 Using the threshold '''L = 60''', what is the probability that the fish that you pick is actually of type B, but you classify it wrongly as type A.
		+	* 1.4 From the given information, can you find the probability that you make a wrong classification that using '''L=60''' as the threshold? If you can't, what information is missing?
		+	* 1.5 The threshold '''L=60''' might not be the best. What is the best threshold value '''L''' that you can use to classify the fishes?
		+	* 1.6 Using the threshold that you proposed, what is the probability that the fish that you pick is actually of type A, but you classify it wrongly as type B.
		+	* 1.7 Using the threshold that you proposed, what is the probability that the fish that you pick is actually of type B, but you classify it wrongly as type A.
		+	* 1.8 From the given information, can you find the probability that you make a wrong classification that using the threshold that you proposed? What is the difference between this situation and the situation in question 1.4.

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 02:58, 9 ตุลาคม 2557
แถว 26:		แถว 26:

	10. The average height that Somchai the athlete can jump is '''2 m''' with variance '''0.16'''. Today to win, Somchai has to jump higher than '''2.4 m'''. What is the approximate probability that Somchai will win?		10. The average height that Somchai the athlete can jump is '''2 m''' with variance '''0.16'''. Today to win, Somchai has to jump higher than '''2.4 m'''. What is the approximate probability that Somchai will win?
		+
		+	== Challenging problems ==

@@ แถว 23: / แถว 23: @@
 . Approximate the minimum value '''a''' such that '''P{ -a <= Z <= a } >= 0.7'''.
-. The download speed of a file to your computer is normally distributed with parameters <math>\mu=5</math> Mbps and <math>\sigma^2 = 0.5</math>.  What is the probability that you get the download speed faster than 6 Mbps?  What is the probability that your speed is below 4 Mbps?
+. The download speed of a file to your computer is normally distributed with parameters '''<math>\mu=5</math>''' Mbps and '''<math>\sigma^2 = 0.5</math>'''.  What is the probability that you get the download speed faster than '''6''' Mbps?  What is the probability that your speed is below '''4''' Mbps?
-. The average height that Somchai the athlete can jump is '''2 m''' with variance 0.16.   Today to win, Somchai has to jump higher than 2.4 m.  What is the approximate probability that Somchai will win?
+. The average height that Somchai the athlete can jump is '''2 m''' with variance '''0.16'''.   Today to win, Somchai has to jump higher than '''2.4 m'''.  What is the approximate probability that Somchai will win?

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 02:55, 9 ตุลาคม 2557
แถว 24:		แถว 24:

	9. The download speed of a file to your computer is normally distributed with parameters <math>\mu=5</math> Mbps and <math>\sigma^2 = 0.5</math>. What is the probability that you get the download speed faster than 6 Mbps? What is the probability that your speed is below 4 Mbps?		9. The download speed of a file to your computer is normally distributed with parameters <math>\mu=5</math> Mbps and <math>\sigma^2 = 0.5</math>. What is the probability that you get the download speed faster than 6 Mbps? What is the probability that your speed is below 4 Mbps?
		+
		+	10. The average height that Somchai the athlete can jump is '''2 m''' with variance 0.16. Today to win, Somchai has to jump higher than 2.4 m. What is the approximate probability that Somchai will win?

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 02:52, 9 ตุลาคม 2557
แถว 22:		แถว 22:

	8. Approximate the minimum value '''a''' such that '''P{ -a <= Z <= a } >= 0.7'''.		8. Approximate the minimum value '''a''' such that '''P{ -a <= Z <= a } >= 0.7'''.
		+
		+	9. The download speed of a file to your computer is normally distributed with parameters <math>\mu=5</math> Mbps and <math>\sigma^2 = 0.5</math>. What is the probability that you get the download speed faster than 6 Mbps? What is the probability that your speed is below 4 Mbps?

@@ แถว 13: / แถว 13: @@
 . Find '''P{ Z >= 1 }'''.
-. Approximate the minimum value '''a''' such that '''P{ Z >= a } <= 0.1'''.
+. Find '''P{ Z >= -0.3 }'''.
-. Approximate the minimum value '''a''' such that '''P{ -a <= Z <= a } >= 0.7'''.
+. Find '''P{ -1 <= Z <= 0.1 }'''.

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 02:45, 9 ตุลาคม 2557
แถว 14:		แถว 14:

	4. Approximate the minimum value '''a''' such that '''P{ Z >= a } <= 0.1'''.		4. Approximate the minimum value '''a''' such that '''P{ Z >= a } <= 0.1'''.
		+
		+	5. Approximate the minimum value '''a''' such that '''P{ -a <= Z <= a } >= 0.7'''.

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 02:43, 9 ตุลาคม 2557
แถว 2:		แถว 2:

	To compute the cdf of standard normal random variable, you can use a table from [http://en.wikipedia.org/wiki/Standard_normal_table wikipedia].		To compute the cdf of standard normal random variable, you can use a table from [http://en.wikipedia.org/wiki/Standard_normal_table wikipedia].
		+
		+	== Basic practice ==
		+
		+	Let '''Z''' be a standard normal random variable (whose mean is 0 and variance is 1).
		+
		+	1. Find '''P{ Z >= 0 }'''.
		+
		+	2. Find '''P{ Z >= 0.5 }'''.
		+
		+	3. Find '''P{ Z >= 1 }'''.
		+
		+	4. Approximate the minimum value '''a''' such that '''P{ Z >= a } <= 0.1'''.