There are two players in the game. Each player can pick any integer number between 1 and n. If two numbers are the same then player 1 pays 1 dollar to player 2. If two numbers are different than nothing happens.
(a) Prove that there are no equilibria in pure strategies;
(b) Prove that in the equilibrium each strategy should be played with a positive probability.
(c) Find all NE of the game.
In: Statistics and Probability
A motorist makes three driving errors, each independently resulting in an accident with probability 0.25.
Each accident results in a loss that is exponentially distributed with mean 0.80. Losses are mutually independent and independent of the number of accidents.
The motorist's insurer reimburses 70% of each loss due to an accident.
Calculate the variance of the total unreimbursed loss the motorist experiences due to accidents resulting from these driving errors
In: Statistics and Probability
If you bet $1 in Kentucky’s Pick 4 lottery, you either lose $1 or gain $4999. (The winning prize is $5000, but your $1 bet is not returned, so the net gain is $4999.) The game is played by selecting a four-digit number between 0000 and 9999. What is the probability of winning? If you bet $1 on 1234, what is the expected value of your gain or loss?
In: Statistics and Probability
We produce a random real number X through the following two-stage experiment. First roll a fair die to get an outcome Y in the set {1, 2, . . . , 6}. Then, if Y = k, choose X uniformly from the interval (0, k]. Find the cumulative distribution function F(s) and the probability density function f(s) of X for 3 < s < 4.
In: Statistics and Probability
For one statistics course, among the students who purchase
textbook, 60% choose physical textbook, 40% choose electronic
textbook. Assume three students who made the purchase are randomly
selected. Let random variable X be the number of students chosen
physical textbook.
1.(6) find the probability distribution of X.
2.(4) Find the mean of and the standard deviation of X
In: Statistics and Probability
A day’s production of 850 parts contains 50 defective parts. Three parts are selected at random without replacement. Let the random variable ? equal the number of defective parts in the sample.
1. Find the probability mass function
2. Find the cumulative distribution function of ?.
3. Find ?(? > 0.5) =
4. Find ?(1.5) =
5. Find ?(2) − ?(0.3) =
6. Find ?(0.99 < ? < 2.5) =
In: Statistics and Probability
According to a report by the Commerce Department in the fall of 2004, 20% of U.S. households had some type of high-speed Internet connection. Let Nn denote the number of U.S. households with a high-speed Internet connection in n households. What is the probability that 20 of the first 200 households surveyed have high-speed Internet given that 5 of the first 75 households surveyed have it?
In: Statistics and Probability
|
A. The Appliance Center has six sales representatives at its North Jacksonville outlet. Listed below is the number of refrigerators sold by each last month. |
| Sales Representative | Number Sold |
||
| Zina Craft | 56 | ||
| Woon Junge | 50 | ||
| Ernie DeBrul | 52 | ||
| Jan Niles | 49 | ||
| Molly Camp | 49 | ||
| Rachel Myak | 53 | ||
| How many samples of size 2 are possible? |
| No of samples |
| . |
Select all possible samples of size 2 and compute the mean number sold. (Round Mean values to 1 decimal place.) |
| Sold | Mean |
| (Click to select)56,4956,5056,5249,5350,49 | |
| (Click to select)56,5256,5050,4956,4949,53 | |
| (Click to select)56,4956,5250,4949,5356,50 | |
| (Click to select)49,5356,5250,4956,5056,49 | |
| (Click to select)56,5349,5349,4956,4956,50 | |
| (Click to select)56,4950,5249,5349,4956,50 | |
| (Click to select)49,5350,4956,4949,4956,50 | |
| (Click to select)50,4949,5356,5049,4956,49 | |
| (Click to select)56,5056,4949,5350,5349,49 | |
| (Click to select)52,4949,4956,4949,5356,50 | |
| (Click to select)49,4949,5356,5056,4952,49 | |
| (Click to select)56,4949,5350,4952,5356,50 | |
| (Click to select)56,5049,5356,4949,4956,52 | |
| (Click to select)56,5056,4950,5349,5356,52 | |
| (Click to select)56,5056,5252,5356,4949,53 | |
|
What is the mean of the population? What is the mean of the sample means? (Round your answers to 2 decimal places.) |
| Mean of sample mean | |
| Population mean | |
| What is the shape of the distribution of the sample mean? | |||||
|
B.
|
Power+, Inc. produces AA batteries used in remote-controlled toy cars. The mean life of these batteries follows the normal probability distribution with a mean of 38 hours and a standard deviation of 5.9 hours. As a part of its quality assurance program, Power+, Inc. tests samples of 16 batteries. |
| What can you say about the shape of the distribution of the sample mean? | |||||||
|
| ) |
What is the standard error of the distribution of the sample mean? (Round your answer to 4 decimal places.) |
| Standard error |
|
What proportion of the samples will have a mean useful life of more than 39 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.) |
| Probability |
| ) |
What proportion of the sample will have a mean useful life greater than 36.5 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.) |
| Probability |
|
What proportion of the sample will have a mean useful life between 36.5 and 39 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.) |
| Probability |
C.
|
Crossett Trucking Company claims that the mean weight of its delivery trucks when they are fully loaded is 6,856 pounds and the standard deviation is 105 pounds. Assume that the population follows the normal distribution. Forty six trucks are randomly selected and weighed. Within what limits will 95% of the sample means occur? (Round your answers to the nearest whole number.) |
| The limits are | and |
In: Statistics and Probability
|
A. The Appliance Center has six sales representatives at its North Jacksonville outlet. Listed below is the number of refrigerators sold by each last month. |
| Sales Representative | Number Sold |
||
| Zina Craft | 56 | ||
| Woon Junge | 50 | ||
| Ernie DeBrul | 52 | ||
| Jan Niles | 49 | ||
| Molly Camp | 49 | ||
| Rachel Myak | 53 | ||
| How many samples of size 2 are possible? |
| No of samples |
| . |
Select all possible samples of size 2 and compute the mean number sold. (Round Mean values to 1 decimal place.) |
| Sold | Mean |
| (Click to select)56,4956,5056,5249,5350,49 | |
| (Click to select)56,5256,5050,4956,4949,53 | |
| (Click to select)56,4956,5250,4949,5356,50 | |
| (Click to select)49,5356,5250,4956,5056,49 | |
| (Click to select)56,5349,5349,4956,4956,50 | |
| (Click to select)56,4950,5249,5349,4956,50 | |
| (Click to select)49,5350,4956,4949,4956,50 | |
| (Click to select)50,4949,5356,5049,4956,49 | |
| (Click to select)56,5056,4949,5350,5349,49 | |
| (Click to select)52,4949,4956,4949,5356,50 | |
| (Click to select)49,4949,5356,5056,4952,49 | |
| (Click to select)56,4949,5350,4952,5356,50 | |
| (Click to select)56,5049,5356,4949,4956,52 | |
| (Click to select)56,5056,4950,5349,5356,52 | |
| (Click to select)56,5056,5252,5356,4949,53 | |
|
What is the mean of the population? What is the mean of the sample means? (Round your answers to 2 decimal places.) |
| Mean of sample mean | |
| Population mean | |
| What is the shape of the distribution of the sample mean? | |||||
|
B.
|
Power+, Inc. produces AA batteries used in remote-controlled toy cars. The mean life of these batteries follows the normal probability distribution with a mean of 38 hours and a standard deviation of 5.9 hours. As a part of its quality assurance program, Power+, Inc. tests samples of 16 batteries. |
| What can you say about the shape of the distribution of the sample mean? | |||||||
|
| ) |
What is the standard error of the distribution of the sample mean? (Round your answer to 4 decimal places.) |
| Standard error |
|
What proportion of the samples will have a mean useful life of more than 39 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.) |
| Probability |
| ) |
What proportion of the sample will have a mean useful life greater than 36.5 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.) |
| Probability |
|
What proportion of the sample will have a mean useful life between 36.5 and 39 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.) |
| Probability |
C.
|
Crossett Trucking Company claims that the mean weight of its delivery trucks when they are fully loaded is 6,856 pounds and the standard deviation is 105 pounds. Assume that the population follows the normal distribution. Forty six trucks are randomly selected and weighed. Within what limits will 95% of the sample means occur? (Round your answers to the nearest whole number.) |
| The limits are | and |
In: Statistics and Probability
The experiment of rolling a fair six-sided die twice and looking at the values of the faces that are facing up, has the following sample space.
For example, the result (1,2) implies that the face that is up from the first die shows the value 1 and the value of the face that is up from the second die is 2.
sample space of tossing 2 die
A pair of dice is thrown.
Let X = the number of multiples of 2.
Complete the table to construct a probability distribution for X using the sample space from the experiment of rolling two fair six-sided dice.
Note: Your answers should be approximate decimals to 4 places.
|
X |
P(x) |
|
0 |
|
|
1 |
|
|
2 |
Probability distribution for X = num. of multiples of
2
In: Statistics and Probability