Find the stationary distribution of this chain

Suppose that the probability it rains today is 0.3 if neither of the last two days was rainy, but 0.6 if at least one of the last two days was rainy. Let the weather on day n, Wn, be R for rain, or S for sun. Wn is not a Markov chain, but the weather for the last two days Xn = (Wn−1 , Wn ) is a Markov chain with four states {RR, RS, SR, SS}.

Suppose MPC is 0.3, use the spending multiplier to fill in the values for an autonomous government spending of $700.

What are some of the problems with the spending multiplier?

(10 Points)

[You must review the literature about the multiplier]

Let A =

| 0.4 −0.3 |

| 0.4 1.2 |

Analyze the long-term behavior of Ak , i.e., lim k→+∞ Ak .

1. In testing the null hypothesis that p = 0.3 against the alternative that p not equal 0.3, the probability of a Type II error is _____________ when p = 0.4 than when p = 0.6.

a. the same

b. smaller

c. larger

d. none of the above

2. During the pre-flight check, Pilot Jones discovers a minor problem - a warning light indicates that the fuel guage may be broken. If Jones decides to check the fuel level by hand, it will delay the flight by 45 minutes. If Jones decides to ignore the warning, the aircraft may run out of fuel before it gets to Gimli. In this situation, what would be:

i) the appropriate null hypothesis? and;
ii) a type I error?

Question 2 options:

A 0.3 Kg ball is initially at rest at the top left side of a frictionless incline plane: The incline is 0.25 m height and has a length of 0.65 m.

a) What is the initial Gravitational Potential Energy of the Ball at the top of the incline? b) What will be the final Kinetic energy of the ball at the bottom right side of the incline? c) If there were friction between the ball and the incline, what would happen to the final Kinetic energy of the ball at the bottom of the incline? Increase, decrease, or states the same?

1. Two stocks have the following return distributions.

Do the necessary analysis and determine which stock is a better choice for a risk-averse investor.

A cell is immersed in water at 0 ^o C for a considerable period of time. It is then taken out and the contents of its vacuole are found to be approximately 0.2 M sucrose [assume this is the overall molarity for the cell].

            (a) At equilibrium, what was the cell's Y_p?

            (b) What would its Y_p have been had it contained 0.2 M NaCl?

Melanoma treatment. An experiment evaluated the use of genetically engineered white blood cells in the treatment of patients with melanoma.^y Patients were divided into three cohorts. Patient cohort 1 received genetically engineered lymphocytes that were cultured ex vivo for 19 days. Cohort 2 received cells that were cultured for between 6 and 9 days. Cohort 3 received cells that were generated by a second rapid expansion performing after 8 to 9 days. Cell doubling times were as follows.

Cohort 1               8.7          11.9        10.0

Cohort 2               11.4        1.0          1.3          1.0          2.0          0.6          0.8          0.7          0.9          1.9

Cohort 3               0.9          3.3          1.2          1.1

Either create a file with these data or download the file MORGAN2006.* from the companion website. Most statistical programs require you to enter that data into two columns: one column for the explanatory variable (COHORT) and the other for the response variable (DOUBLING). Your final data table should have 2 columns and 18 rows.

If you do not have access to a statistical program, consider using BrightStat. com.^z Use of BrightStat.com is free. However, you must register as a user in order to access its ANOVA features.

(a)   Calculate the means, standard deviations, and sample sizes of each group. Use the “double the standard deviation” benchmark to assess whether group variances are significantly different. Is there evidence of heteroscedasticity?

(b)   Conduct Levene’s test for unequal variance. Show all hypothesis testing steps. What do you conclude?

In a recent survey concerning company sales and net earnings, 15 companies responded with the following information.

a) Using a statistical computing tool, find the equation of the regression line.
For full marks your answer should be accurate to at least three decimal places.

ŷ = ? + ?x

b) Use the regression line from part a to estimate the net earnings for a company with sales of $54.8 thousand.
For full marks your answer should be accurate to at least one decimal place.

Earnings: ?

A consumer products company has identified a potential product which would require $1,800,000 in start-up costs to launch. If it turns out to be a major success, there will be a $10,000,000 contribution to profit. A minor success would give a profit contribution of $2,000,000, while a failure would have a profit contribution of only $500,000. The company is most worried about this third possibility, since in this case the net profit would be $500,000 minus $1,800,000, i.e. a loss of $1,300,000. In the past, only one new product in twenty became a major success, while three-quarters of them became failures; there is no reason to suspect that this product would be any different from the rest. Some of their competitors use an outside independent market research firm to give them advice about new products. The fee for the research firm is $50,000; in return, the consumer products company would be told that the proposed product either “looks well” or “looks poorly”. The research company had established a track record which gave them confidence about saying the following: 1. If a product would be a major success, they would say “looks well” with probability 0.8; 2. If a product would be a minor success, they would say “looks poorly” with probability 0.7; 3. If a product would be a failure, they would say “looks poorly” with proba- bility 0.9. Develop a decision tree and solve it to obtain a recommendation for the con- sumer products company. Show all workings and calculations