Problem 3

Assume that the probability of rain tomorrow is 0.5 if it is raining today, and assume that the probability of its being clear (no rain) tomorrow is 0.9 if it is clear today. Also assume that these probabilities do not change if information is also provided about the weather before today.

a) Find the n-step transition matrix for n = 3, 7, 10, 20.

b) The probability of rain today is 0.5 Use the results in the part (a) to determine the probability that it rains in n days, for n = 3, 7, 10, 20.

c) Formulate the steady-state equations to obtain the steady state probabilities for this process. Compare the probabilities of the transition matrices of n steps of part (a) with these of the steady state as n grows.

A terrible despot governing one small country decided to check
how smart are people living in his country. He gathered 20 smartest people
and put hats on their heads. Everybody could see all hats except their own.
Then the despot said: "Some of the hats have a red stripe on them. I will
give you one minute to think and then ask who has a red stripe on their
hat? If nobody answers, then I will give one more minute and ask the same
question again. I will repeat it 100 times. If you guess somehow that you got
stripe on the hat you have to wait till I ask my question and say immediately
about that, because after somebody will gure out correctly that he or she
has a stripe on the hat, I will kill everybody else who has the stripe and did
not gure it out. If you say that you have a stripe and you don't , I will kill
you. " They know that each of them is really good at deduction (got A for
Math 311W when they were in college) and nobody wants to die.
a) Prove that if 2 people have red stripes on their hats, then after the terrible
despot will ask them second time all of them will say that they have them,
and despot won't be able to kill anybody.
b) What happens if three people have stripes?

The NASW Code of Ethics makes a number of statements about social workers’ responsibility to study, use, and engage in research and evaluation. In the past, many social workers had difficulty thinking of themselves as knowledgeable and capable in research, despite completing the required research course in school. Think of yourself as a part of a new breed of social workers. You are completing your education at a point in time that places great emphasis on both research and evaluation. You also have greater access to published research than ever before. Research knowledge and skills are like muscles—if you do not use them, they will atrophy. You have an ethical obligation as a social worker to exercise and flex your research muscle. Consider how the NASW Code of Ethics guides your professional research.

Post an analysis of how you would present the results of the evaluation to a group of social work colleagues. Identify the background information that you think they would need and the key message of your presentation. Explain the strategies that you might use to meet your colleagues’ interests and goals. Identify questions that your colleagues might have and what their reactions might be.

b. An individual obtains a car loan whim pays $30,000. The loan will he paid off in 3
years, and payments are made monthly. Interest rate on the loan is 7%, and compounding is monthly.

1. Find the amount of monthly payments to pay the loan off. Provide a complete
amortization schedule of the loan ( this will entail a long table containing 37 rows).
2. Present your work in detail and explain. Provide references for content. (Excel sheet required).

An urn contains 5 red balls, 4 green balls and 4 yellow balls, for a total of 13 balls.

if five balls are randomly selected without replacement, what is the probability of selecting at least two red balls, given that at least one yellow ball is selected?

6. You wanted to buy lettuce for your salad. In the grocery store, you found a head of lettuce in the fresh vegetable section. You also found a sealed bag of pre-packaged refrigerated lettuce. Answer the following questions based on these two types of lettuces. a. In their original condition (unopened package in refrigerated condition vs fresh head of lettuce in ambient condition), which one would deteriorate faster? Explain your answer. (2 points) b. How the gas composition of the sealed bag of pre-packaged refrigerated lettuce is modified? Explain the advantage and disadvantages of such packaging. (4 points) c. You bought the fresh head of lettuce and kept it in the refrigerator for storage. However, due to lack of space, you put it in the fruit tray with some fruits. Is this a good idea? Why or why not? (2 points) d. Over a period of time in the refrigerator you noticed wilting of the lettuce. What could be the reason? (2 points)

class A

{

public:

//constructors //

other members private:

int a;

int b;

};

Give declatations of operator functions for each of the following ways to overload operator + You must state where the declatation goes, whether within the class in the public or private section or outside the class. The operator + may be overloaded. a) as friend function b) as member function c) as non-friend, non-member function

Read the posted articles about Baby Storm and the parents' decision to raise her without a gender. Given what you have learned about biological, social, and cognitive influences on gender development, is raising a gender-neutral child possible? Or desirable? Or perhaps even harmful? Be sure you explain your argument!

The Equation of motion for the standard mass-spring-damper system is

Mẍ + Bẋ + Kx = f(t).

Given the parameters {M = 2kg, B = 67.882 N-s/m, K = 400 N/m}, determine the free response of the system to initial conditions { x₀ = -1m, v₀ = 40 m/s}. To help verify the correctness of your answer, a plot of x(t) should go through the coordinates {t, x(t)} = {.015, -0.5141} and {t, x(t)} = 0.03, -0.2043}.

Numerically simulate the response of the system using the Matlab function ode45. Plot the displacement of the mass as a function of time for the first 0.5s. Use a time-resolution of 0.001s (have ode45 return values of x(t) at 1ms intervals). This plot should be a solid black line with a LineWidth of 3.

“Hold” the plot and superimpose the two points listed above (the two {t, x(t)} pairs). Use red circles to show those points. Make the circles’ Markersize of 10 and LineWidth of 3.

Determine the exact analytic (“hand”) solution to the problem. Use Matlab to calculate the values of that solution at 0.05s time steps. Superimpose that data on top of the numerical solution (and the two red circles) using blue diamonds with the same Markersize and LineWidth parameters as for the circles.