Probstat/week5 practice 1 - ประวัติรุ่นแก้ไข

Jittat: /* Practice exercises */

2014-09-16T06:57:15Z

Practice exercises

Jittat: /* Distribution of the binomial random variables */

2014-09-16T05:42:32Z

Distribution of the binomial random variables

Jittat: /* Distribution of the binomial random variables */

2014-09-16T05:39:08Z

Distribution of the binomial random variables

Jittat: /* Distribution of th binomial random variables */

2014-09-16T05:36:42Z

Distribution of th binomial random variables

Jittat: /* Geometric random variables */

2014-09-16T04:19:06Z

Geometric random variables

Jittat: /* Geometric random variables */

2014-09-16T04:14:42Z

Geometric random variables

Jittat: /* Geometric random variables */

2014-09-16T03:39:01Z

Geometric random variables

Jittat: /* Geometric random variables */

2014-09-16T03:37:51Z

Geometric random variables

Jittat: /* The fullest bins */

2014-09-16T03:21:17Z

The fullest bins

Jittat: /* Binomial and geometric random variables */

2014-09-16T03:01:06Z

Binomial and geometric random variables

@@ แถว 3: / แถว 3: @@
 == Practice exercises ==
 === Variances ===
-. Consider a random variable ''Z'' that becomes 1 with probability 1/3, 0 with probability 1/3, and 1 with probability 1/3.  Find E[''Z''], and ''Var(Z)''.
+. Consider a random variable ''Z'' that becomes -1 with probability 1/3, 0 with probability 1/3, and 1 with probability 1/3.  Find E[''Z''], and ''Var(Z)''.
 . Let random variable ''X'' be the outcome after tossing a fair die (with 6 faces of values 1,2,3,...,6).  Find E[''X''] and ''Var(X)''.

@@ แถว 46: / แถว 46: @@
 Try to plot the pmf of the binomial random variables with the following parameters.
-* n = 10.  (Try to plot them in the same graphs)
+* n = 10.  (Try to plot them in the same graph.)
 ** n = 10, p = 0.5
 ** n = 10, p = 0.7
 ** n = 10, p = 0.9
-* n = 100. (Try to plot them in the same graphs)
+* n = 100. (Try to plot them in the same graph.)
 ** n = 100, p = 0.5
 ** n = 100, p = 0.2
 ** n = 100, p = 0.1

@@ แถว 46: / แถว 46: @@
 Try to plot the pmf of the binomial random variables with the following parameters.
-* n = 10, p = 0.5
+* n = 10.  (Try to plot them in the same graphs)
-* n = 10, p = 0.7
+** n = 10, p = 0.5
-* n = 10, p = 0.9
+** n = 10, p = 0.7
-* n = 100, p = 0.5
+** n = 10, p = 0.9
 * n = 100, p = 0.2
-* n = 100, p = 0.1
+* n = 100. (Try to plot them in the same graphs)

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 05:36, 16 กันยายน 2557
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	For each value of ''n'', perform 10 independent experiments and record the average maximum load, the minimum ''X'' (over these 10 experiments), and the minimum ''X'' (over these 10 experiments). Plot a graph. See how the values of ''X'' grow.		For each value of ''n'', perform 10 independent experiments and record the average maximum load, the minimum ''X'' (over these 10 experiments), and the minimum ''X'' (over these 10 experiments). Plot a graph. See how the values of ''X'' grow.

−	=== Distribution of th binomial random variables ===	+	=== Distribution of the binomial random variables ===
		+	Try to plot the pmf of the binomial random variables with the following parameters.
		+
		+	* n = 10, p = 0.5
		+	* n = 10, p = 0.7
		+	* n = 10, p = 0.9
		+	* n = 100, p = 0.5
		+	* n = 100, p = 0.2
		+	* n = 100, p = 0.1

@@ แถว 27: / แถว 27: @@
 . You start tossing a coin.  You repeatedly toss a coin until you get the same coin as the most recent previous toss.  For example if your first toss is head and the second toss is tail, you will stop at the third toss if you get a tail.  (Note that you definitely make the first two tosses.)  What is the expected number of coin tosses that you have to make.
-.
+. In a certain game there are 2 stages. You have the probability 0.3 of passing the first stage, and probability of 0.2 of passing the second stage.  Passing any stages are independent events.  Playing the game for 1 round on any stage takes 10 minutes.
 == Theoretical exercises ==

@@ แถว 17: / แถว 17: @@
 === Geometric random variables ===
-. You toss a fair die.  You will stop when you the die shows up with a value larger than 4.  What is the expected number of tosses?
+. You toss a fair die.  You will stop when you the die shows up with a value larger than 4.
 . You are the first person in the hat experiment, so you do not want to be part of it.  There are ''n'' hats in the hat locker room and your hat is one of them.  You randomly pick a hat, if it is your hat you will keep it and go home happy.  If it is not your hat, you return the hat to the room and keep randomly picking another hat.  What is the expected number of times you have to pick the hats until you can go home.

@@ แถว 32: / แถว 32: @@
 == Programming exercises ==
 === The fullest bins ===
 === Distribution of th binomial random variables ===

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 03:01, 16 กันยายน 2557
แถว 15:		แถว 15:

	3. An airline knows that a passenger will miss the flight independently with probability 0.05. Given an airplane with the capacity of 300 passengers, the airline would like to allow over-booking, i.e., it will allow the booking of more than 300 passengers. However, if they allow too many extra passengers, it might be the case that more than 300 passengers show up and they run into problems. What should be the number of extra passengers that the airline should allow to make sure that with probability at least 0.95, no more than 300 passengers will show up? ('''Notes:''' in this problem, to figure out the right value, it might be useful to write a computer program.)		3. An airline knows that a passenger will miss the flight independently with probability 0.05. Given an airplane with the capacity of 300 passengers, the airline would like to allow over-booking, i.e., it will allow the booking of more than 300 passengers. However, if they allow too many extra passengers, it might be the case that more than 300 passengers show up and they run into problems. What should be the number of extra passengers that the airline should allow to make sure that with probability at least 0.95, no more than 300 passengers will show up? ('''Notes:''' in this problem, to figure out the right value, it might be useful to write a computer program.)
		+
		+	=== Geometric random variables ===
		+	1.
		+
		+	2.
		+
		+	3.
		+
		+	4.

	== Theoretical exercises ==		== Theoretical exercises ==