The number of students using the math lab per day is found in the distribution below. Find the mean, variance, and standard deviation for this probability distribution ? 6 8 10 12 14 ?(?) 0.15 0 0.35 0.1 … Find the (i) Missing probability

Marge and Homer want to rent a movie but they cannot decide what to watch. Marge wants to watch a drama, whereas Homer wants a comedy. They decide to choose randomly by playing a game. On the count of three, Marge and Homer show one or two fingers. If the sum of fingers is odd, Marge wins and they rent a drama. If the sum of fingers is even, Homer wins and they rent a comedy. Each has a payoff of 4 for winning and 1 for losing.

1. Draw the game table.

2. Find all mixed-strategy Nash equilibria of this game. Explain how you find them clearly.

3. Calculate expected payoff of each player for the mixed-strategy Nash equilibria you have found

   in part b.

4. Graph the best response curves of Marge and Homer on a p-q coordinate plane. Mark all Nash

equilibria.

Java programming

One of the most popular games of chance is a dice game known as “craps,” which is played in casinos and back alleys throughout the world.

The rules of the game are straightforward:

A player rolls two dice. Each die has six faces. These faces contain 1, 2,3,4,5, and 6 spots. After the dice have come to rest, the sum of the spots on the two upward faces is calculated. If the sum is 7 or 11 on the first throw, the player wins. If the sum is 2, 3, or 12 on the first throw (called “craps”), the player loses (i.e., the “house” wins). If the sum is 4, 5,6,8,9, or 10 on the first throw, then that sum becomes the player’s “points.” To win, you must continue rolling the dice until you “make your points.” The player loses by rolling a 7 before making the points.

The objective of this assignment is to implement the tic-tac-toe game with a C program.
The game is played by two players on a board defined as a 5x5 grid (array). Each board
position can contain one of two possible markers, either ‘X’ or ‘O’. The first player plays with
‘X’ while the second player plays with ‘O’. Players place their markers in an empty position of
the board in turns. The objective is to place 5 consecutive markers of the same type in a line (a
line can be any row, any column or any diagonal). The first player who manages to place 5
markers in a line wins. The game is played until one of the players wins or until the board is full
with no player having 5 markers in a line (i.e., the result of the game is a draw).

An athletic footwear company is attempting to estimate the sales that will result from a television advertisement campaign of its new athletic shoe. The contribution to earnings from each pair of shoes sold is $40. Suppose that the probability that a television viewer will watch the advertisement (as opposed to turn his/her attention elsewhere) is 0.40. Furthermore, suppose that 1% of viewers who watch the advertisement on a local television channel will buy a pair of shoes. The company can buy television advertising time in one of the time slots according to Table below:

(a) Suppose that the company decides to buy one minute of advertising time. Which time slot would yield the highest expected contribution to earnings net of costs? What is the total expected contribution to earnings resulting from the advertisement?

(b) Suppose the company decides to buy two one-minute advertisements in different time slots. Which two different time slots should the company purchase to maximize the expected contribution to earnings? What is the total expected contribution to earnings resulting from these two advertisements?

Can someone please answer these two by Friday?

Problem 3 Five men and five women are ranked according to their scores on an examination. Assume that no two scores are alike, and all 10! possible rankings are equally likely. Let X denote the highest ranking achieved by a woman (for example, X = 2 if the top-ranked person was a man, and the next-ranked person was a woman). Find the probability mass function (pmf) of the random variable X, and plot the cumulative distribution function (cdf) of X.

Problem 4 Suppose there are three cards numbered 2, 7, 10, respectively. Suppose you are to be offered these cards in random order. When you are offered a card, you must immediately either accept it or reject it. If you accept a card, the process ends. If you reject a card, then the next card (if there is one) is offered. If you reject the first two cards, you have to accept the final card. You plan to reject the first card offered, and then to accept the next card if and only if its value is greater than the value of the first card. Let X be a number on the card you have accepted in the end. Find the pmf of X and plot the cdf of X.

In the context of total quality management (TQM), which of the following statements is true of continuous improvement?

a.The basic philosophy of continuous improvement is that improving major processes periodically has the highest probability of success.

b.It is the implementation of a large number of small, incremental improvements in all areas of an organization on an ongoing basis.

c.In continuous improvement, changes to all job activities are made solely by the founders and top-level executives.

d.In continuous improvement, managers measure the expected benefits of a huge change and favor the ideas with the biggest payoffs.

In the context of budgetary control, a responsibility center is defined as any organizational department or unit under the supervision of a team of 6 to 12 employees responsible for its activity.

True

False

Lucas uses a fitness tracker app on his smartphone to measure his calorie intake in a day and track the activities that help him burn calories through the day. His aim is to modify his lifestyle for better health and increased work productivity. In the context of managing quality and performance, Lucas's practice of voluntarily collecting and analyzing data about himself in order to improve is an example of:

a.auto-analytics.

b.self-induction.

c.a feasibility study.

d.a social orientation approach.

Education. Post-secondary educational institutions in the United States (trade schools, colleges, universities, etc.) traditionally offer four different types of degrees or certificates. The U.S. Department of Education recorded the highest degree granted by each of these institutions in the year 2003. The percentages are shown in the table below. A random sample of 300 institutions was taken in 2013 and the number of institutions in the sample for each category is also shown in the table. Conduct a hypothesis test to determine whether there has been any change from the percentages reported in 2003. Round all calculated values to four decimal places.

a. Enter the expected values for the hypothesis test in the table below.

b. Calculate the test statistic for this hypothesis test.  ? z t X^2 F  =

c. Calculate the degrees of freedom for this hypothesis test.

d. Calculate the p-value for this hypothesis test. p-value =

e. What is your conclusion using αα = 0.01?

A. Reject H0H0
B. Do not reject H0H0

5. The number of daily texts sent by Marymount students are normally distributed with a mean of 80 texts and a standard deviation of 50 texts.

(a) Find the probability that a randomly selected Marymount student sends more than 100 texts each day.

(b) Find the probability that 25 randomly selected Marymount students will have a mean number of daily texts sent that is greater than 50 texts.

(c) Suppose a parent wants their child in the bottom 25% of texters. Find the cut-off value for the number of texts below which 25% of MCU students lie.

if possible include graph