Find the function with the maclaurin series

- 1); I{x>1}, theta > 1. (a) Show that log Xi has an exponential distribution with a mean of 1/theta. (b) Find the form for a UMP test of H_0: theta <= theta_0 vs. H_a : theta > theta_0. (c) Give formula for nding the rejection region for a given value of alpha. Hint: use the result from (a) to find the distribution of the test statistic. (d) Conduct the test in (b) with alpha = 0.05 and theta_0 = 1:5 using the dataset: {1.2, 2.4, 1.3, 1.7, 1.9}. (e) Find the form of a UMPU test for testing H_0 : theta = theta_0 vs. H_a : theta_0 != theta_0. (f) Use the data in (d) to conduct the test in (e) with alpha = 0.05 and theta_0 = 1.5.

- 1); I{x>1}, theta > 1. (a) Show that log Xi has an exponential distribution with a mean of 1/theta. (b) Find the form for a UMP test of H_0: theta <= theta_0 vs. H_a : theta > theta_0. (c) Give formula for nding the rejection region for a given value of alpha. Hint: use the result from (a) to find the distribution of the test statistic. (d) Conduct the test in (b) with alpha = 0.05 and theta_0 = 1:5 using the dataset: {1.2, 2.4, 1.3, 1.7, 1.9}. (e) Find the form of a UMPU test for testing H_0 : theta = theta_0 vs. H_a : theta_0 != theta_0. (f) Use the data in (d) to conduct the test in (e) with alpha = 0.05 and theta_0 = 1.5.

- 1); I{x>1}, theta > 1. (a) Show that log Xi has an exponential distribution with a mean of 1/theta. (b) Find the form for a UMP test of H_0: theta <= theta_0 vs. H_a : theta > theta_0. (c) Give formula for nding the rejection region for a given value of alpha. Hint: use the result from (a) to find the distribution of the test statistic. (d) Conduct the test in (b) with alpha = 0.05 and theta_0 = 1:5 using the dataset: {1.2, 2.4, 1.3, 1.7, 1.9}. (e) Find the form of a UMPU test for testing H_0 : theta = theta_0 vs. H_a : theta_0 != theta_0. (f) Use the data in (d) to conduct the test in (e) with alpha = 0.05 and theta_0 = 1.5.

ptember there are 12 hours of sunlight, and in December there are 10 hours of sunlight. Find a function for the average sunlight L(t) as a function of time, t, in months. Assume t = 0 is January and the number of hours of sunlight varies over the period of a year. b) What is the average amount of daylight in October?

subgame perfect Nash equilibrium? Question 3: In which situations should we need the mixed extension of a game? Question 4: Find, if any, all Nash equilibria of the following famous matrix game: L R U (2,0) (3,3) D (3,4) (1,2) Question 5: What is the difference between a separating equilibrium and a pooling equilibrium in Bayesian games? Question 6: Give another name for, if it exists, the intersection of the players’ best-response « functions » in a game? Question 7: assuming we only deal with pure strategies, the Prisoner’s Dilemma is a situation with: No Nash equilibrium One sub-optimal Nash equilibrium One sub-optimal dominant profile No dominant profile Question 8: If it exists, a pure Nash equilibrium is always a profile of dominant strategies: True False Question 9: All games have at least one pure strategy Nash equilibrium: True False Question 10: If a tree game has a backward induction equilibrium then it must also be a Nash equilibrium of all of its subgames: Tr 2/2 Question 11: The mixed Nash equilibrium payoffs are always strictly smaller than the pure Nash equilibrium payoffs: True False Question 12: Which of the following statements about dominant/dominated strategies is/are true? I. A dominant strategy dominates a dominated strategy in 2x2 games. II. A dominated strategy must be dominated by a dominant strategy in all games. III. A profile of dominant strategies must be a pure strategy Nash equilibrium. IV. A dominated strategy must be dominated by a dominant strategy in 2x2 games. I, II and IV only I, II and III only II and III only I and IV only I, III and IV only I and II only Question 13: A pure strategy Nash equilibrium is a special case of a mixed strategy Nash equilibrium: True False Question 14: Consider the following 2x2 matrix game: L R U (3,2) (2,4) D (-1,4) (4,3) The number of pure and mixed Nash equilibria in the above game is: 0 1 2 3 Exercise (corresponding to questions 15 to 20 below): assume a medical doctor (M) prescribes either drug A or drug B to a patient (P), who complies (C) or not (NC) with each of this treatment. In case of compliance, controlled by an authority in charge of health services quality, the physician is rewarded at a level of 1 for drug A and 2 for drug B. In case of noncompliance, the physician is « punished » at -1 level for non-compliance of the patient with drug A and at -2 level for non-compliance with drug B. As for the compliant patient, drug A should give him back 2 years of life saved and drug B, only 1 year of life saved. When noncompliant with drug A, the same patient wins 3 years of life (due to avoiding unexpected allergic shock for instance), and when non-compliant with drug B, the patient loses 3 years of life. Question 15: You will draw the corresponding matrix of the simultaneous doctor-patient game. Question 16: Find, if any, the profile(s) of dominant strategies of this game. Question 17: Find, if any, the pure strategy Nash equilibrium/equilibria of this game. Question 18: Find, if any, the mixed strategy Nash equilibrium/equilibria of this game. Questions 19 and 20: Now the doctor prescribes first, then the patient complies or not: draw the corresponding extensive-form game (= question 19) AND find the subgame perfect Nash equilibrium/equilibria (=

itially, the balloon contains 4 ft3 of hydrogen and it takes 14 seconds to com- pletely fill the balloon. (a) At what rate is the balloon filled? (b) Find a linear function V that models the volume of hydrogen in the balloon at any time t. (c) What can you say about the graph of V ? (You do not need to sketch the graph.)

rts to the fireworks platforms: one part is on the ground and the other part is on top of a building. You are going to graph all of your results on one coordinate plane. Make sure to label each graph with its equation. Use the following equations to assist with this assignment. • The function for objects dropped from a height where t is the time in seconds, h is the height in feet at time it t, and 0 h is the initial height is 2 0 ht t h ( ) 16 =− + . • The function for objects that are launched where t is the time in seconds, h is the height in feet at time t, 0 h is the initial height, and 0 v is the initial velocity in feet per second is 2 0 0 ht t vt h ( ) 16 =− + + . Select the link below to access centimeter grid paper for your portfolio. Centimeter Grid Paper Task 1 First, conduct some research to help you with later portions of this portfolio assessment. • Find a local building and estimate its height. How tall do you think the building is? • Use the Internet to find some initial velocities for different types of fireworks. What are some of the initial velocities that you found? Task 2 Respond to the following items. 1. While setting up a fireworks display, you have a tool at the top of the building and need to drop it to a coworker below. a. How long will it take the tool to fall to the ground? (Hint: use the first equation that you were given above, 2 0 ht t h ( ) 16 =− + . For the building’s height, use the height of the building that you estimated in Task 1.) b. Draw a graph that represents the path of this tool falling to the ground. Be sure to label your axes with a title and a scale. Your graph should show the height of the tool, h, after t seconds have passed. Label this line “Tool”.

and range for its inverse. 2.if a function is graphed you can rotate the graph 90 degrees and you will always get the graph of the inverse 3..making the y cordiantes negative will produce the points on the inverse and my last one isnt a yes or no its a equaion which is useing (f(g(x)) and it says to find the inverse with it and the quations givien are f(x)=3x+4 and g(x)= 1/3x-4/3

consumes each year is 196 with a standard deviation of 22 pounds (Source: American Dietetic Association). If a sample of 50 individuals is randomly selected, find the probability that the mean of the sample will be less than 200 pounds.

find the surface area when the radius is 3 in.