Please solve the following questions. Please show all work and all steps.

1a.) Find CDF of the Bernoulli Distribution.

1b.) Explain your reasoning for part 1a above. Do not use a series result.

2a.) For the geometric distribution, show that the geometric pdf is actually a pdf (all probabilities are greater than or equal to 0 and the sum of the pdf from x=1 to x=infinity is equal to 1).

2b.) Find E(X) for 2a above.

2c.) Find V(X) for 2a above.

Suppose a geyser has a mean time between eruptions of 80 minutes. If the interval of time between the eruptions is normally distributed with standard deviation 26 minutes​, answer the following questions. ​(a) What is the probability that a randomly selected time interval between eruptions is longer than 92 ​minutes? The probability that a randomly selected time interval is longer than 92 minutes is approximately 0.3228. ​(Round to four decimal places as​ needed.) ​(b) What is the probability that a random sample of 8 time intervals between eruptions has a mean longer than 92 ​minutes? The probability that the mean of a random sample of 8 time intervals is more than 92 minutes is approximately nothing. ​(Round to four decimal places as​ needed.)

ONLY ANSWER PART B

What percentage of hospitals provide at least some charity care? Based on a random sample of hospital reports from eastern states, the following information is obtained (units in percentage of hospitals providing at least some charity care):

57.2 56.1 53.1 65.8 59.0 64.7 70.1 64.7 53.5 78.2

Assume that the population of x values has an approximately normal distribution.

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean percentage x and the sample standard deviation s. (Round your answers to one decimal place.)

x = %

s = %

(b) Find a 90% confidence interval for the population average μ of the percentage of hospitals providing at least some charity care. (Round your answers to one decimal place.)

lower limit %

upper limit %

consider the linear programming problem

maximize z = x1 +x2

subjected tp

x1 + 3x2 >= 15

2x1 + x2 >= 10

x1 + 2x2 <=40

3x1 + x2 <= 60

x1 >= 0, x2>= 0

solve using the revised simplex method and comment on any special charateristics of the optimal soultion. sketch the feasible region for the problem as stated above and show on the figure the solutions at the various iterations

You are interested in knowing whether wealthier people are happier. You collected data from fifty people about their incomes and their overall happiness levels on a scale of 1 to 10. Upon analyzing the results, you find that the correlation coefficient has a value of −0.25. On the basis of this data, respond to the following:

• How would you interpret the correlation coefficient in terms of strength and direction?
• How would the results be affected if you increased the number of subjects in the study to one thousand? Why might that affect the overall correlation?
• How important is it to randomly select subjects? Explain in detail using an example of a sample that might not be truly representative of the population.

Write up a short paragraph in your own words, describing what Baye's Theorem is and how is it related to Conditional Probability and the Multiplication Rule. Base on the research, determine what the second fraction would be.

1.14 Let Xn be a Markov chain on state space {1,2,3,4,5} with transition matrix

P=

(a) Is this chain irreducible? Is it aperiodic?

(b) Find the stationary probability vector.

The Army finds that the head sizes (forehead circumference) of soldiers has a normal distribution with a mean of 22.7 inches and a standard deviation of 1.1 inches.

1. Approximately 68% of soldiers have head sizes between (, ) inches.
2. Approximately 95% of soldiers have head sizes between (, ) inches.
3. Approximately 99.7% of soldiers have head sizes between (, ) inches.

What is a dummy variable? If we use one on the right-hand side of the equation in a multivariate analysis, what are the implications for interpreting the constant?  What is multicollinearity? How do we know if we have it in our models? How do we correct for it if we do?  What is hetereskedasticity? Should we really be concerned about it? Why or why not?

Farmers know that driving heavy equipment on wet soil compresses the soil and injures future crops. Here are data on the "penetrability" of the same type of soil at two levels of compression. Penetrability is a measure of how much resistance plant roots will meet when they try to grow through the soil.

Compressed Soil

Intermediate Soil

Use the data, omitting the high outlier, to give a 96% confidence interval for the decrease in penetrability of compressed soil relative to intermediate soil. Compute degrees of freedom using the conservative method.

In your opinion, which calculation is more informative to a primary care physician in a rural village—incidence rates or prevalence rates of HIV? Explain your answer and provide an example to support your response.

The CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as the population mean and assume the population standard deviation of preparation fees is $100.

A) What is the probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean?

B) What is the probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean?

C) What is the probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean?

D) Which, if any of the sample sizes in part (a), (b), and (c) would you recommend to ensure at least a .95 probability that the same mean is withing $16 of the population mean?

simple hypothesis test please be clear with algorithm

The United States and Japan often engage in intense trade negotiations. U.S. officials claim that Japanese manufacturers price their goods higher in Japan than in the United States, in effect subsidizing the low prices in the United States with extremely high prices in Japan. According to the U.S. argument, Japanese manufactures accomplish this by preventing U.S. good from reaching the market.

An economist decides to test the hypothesis that higher retail prices are being charged for automobiles in Japan than in the United States. She obtains independent samples from 50 retail sales in the United States and 50 sales in Japan over the same time. She found the sample average of the U.S. sales to be 26,596 and the sample average of the Japanese sales to be 27,236. The standard deviations were 1,981 and 1,974 respectively.

Using an alpha of 5%, conduct a hypothesis test.

Please solve clearly displaying the following:

What is the null hypothesis?

critical value?

What is the p-value?

declared alpha?

critical value?

Draw a conclusion?

Let X be a random variable representing the number of years of education an individual has, and let Y be a random variable representing an individual’s annual income. Suppose that the latest research in economics has concluded that:

Y = 6X +U

(1)

is the correct model for the relationship between X and Y , where U is another random variable that is independent of X. Suppose Var(X) = 2 and Var(Y ) = 172.

a. Find Var(U).

b. Find Cov(X, Y ) and corr(X, Y ).

c. The variance in Y (income) comes from variance in X (education) and U (other factors unobserved to us). What fraction of the variance in income is explained by variance in education?

d. How does the fraction you found in (c) compare to corr(Y, X)?

2. Let X be exponential with rate lambda. What is the pdf of Y = X^0.5? How about Y = X^3? Contrast the complexity of this result to transformation of a discrete random variable.