Data Distribution Questions and Answers

You fit a CAPM that regresses the excess return of Coca-cola on the excess market return using 20 years of monthly data. You estimate ${\displaystyle \alpha =0,72,\beta =1,37,S^2=20,38,{\sigma }_X^2=19,82\text{and}{\mu }_x=0,71}$.
What is the 99% confidence interval for ${\displaystyle \beta }$?

Among 157 African-American men, the mean systolic blood pressure was 146 mm Hg with a standard deviation of 27. We wish to know if on the basis of these data, we may conclude that the mean systolic blood pressure for a population of African-American is greater than 140. Use ${\displaystyle \alpha =0.01}$.
Solution 1. Data: Variable is systolic blood pressure, ${\displaystyle n=157}$, sample mean ${\displaystyle =146,s=27,\alpha =0.01}$.

In calculating the mode for the grouped data, ${\displaystyle f_0}$ represents

A shot is fired at a very large circular target. The horizontal and vertical coordinates of the point of impact are independent random variables each having a standard normal density. Here the center of the target is taken as the origin. What is the density function of the distance from the center of the target to the point of impact? What are the expected value and the mode of this distance?

The joint distribution of X and Y is as follows.
$$\begin{array}{|ccc|}\hline & & ValuesofY\\ & & 1& 0& P\{X=x\}\\ ValuesofX& 1& 0.1& 0.2& 0.3\\ & 0& 0.3& 0.4& 0.7\\ & P\{Y=y\}& 0.4& 0.6& 1.0\\ \hline\end{array}$$
a. Find the marginal distribution of X and Y.
b. Find the conditional distribution of Y given ${\displaystyle X-1,P\{Y=y\mid X=1\}}$
c. Compute the conditional expectation of Y given ${\displaystyle X=1,E\{Y=y\mid X=1\}}$

Illustrate the inverse transformation method for obtaining a random observation from a given probability distribution?

A Congressional cumittee of three is to be chosen from a set of five Democrats, three Republicans and four independents.
In how many ways can the committee be chosen, if it must have at least one Democrat and at least one Republican?

a. Identify the conditions would it be reasonable to use z-scores to compare the standings of the student on the two tests relative to the other students in the graduating class.
Given info:
The mean SAT math score is 528 with a standard deviation of 105. The mean SAT verbal score is 475 with standard deviation is 98. A student in the graduating class scored 740 on SAT math and 715 on SAT verbal.
b. To identify the test did the student do better.

a. Find Carolinas

To explain: The benefits of representing the data sets using frequency distributions.
To explain: The benefits of representing the data sets using graphs of frequency.

Answer true or false to each of the statements in parts (a) and (b), and explain your reasoning.
a. Two data sets that have identical frequency distributions have identical relative-frequency distributions.
b. Two data sets that have identical relative-frequency distributions have identical frequency distributions.
c. Use your answers to parts (a) and (b) to explain why relativefrequency distributions are better than frequency distributions for comparing two data sets.

(True/False) The central limit theorem implies that:
1.a All variables have bell-shaped sample data distributions if a random sample contains at least 30 observations.
2.b. Population distributions are normal whenever the population size is large.
3.c. For large random samples, the sampling distribution of ${\displaystyle \bar{y}}$ is approximately normal, regardless of the shape of the population distribution.
3.d. The sampling distribution looks more like the population distribution as the sample size increases.

Explain the procedure for constructing frequency distribution for categorical data using Excel.
Explain the procedure for constructing frequency distributions for numerical data using Excel.

Discuss the co efficient of variation also writedown why we use coefficient of variance

z-scores can be used to identify ?, ?, ? values.

Explain TWO strengths in using mean as a measure of central tendency.

The one figure you would request from the given three figures if you are applying for an entry-level job at the large firm and informed of the mean, or mode salary.

Your son has just gotten his driver's license and your bank account is about to get a little (a lot?) lighter. To help mitigate the impact on your finances, you have opted for a high deductible auto insurance policy. The deductible on your policy is $4000, which means that you will pay the first $4000 of any damages and then the insurance will cover the rest. Because of this, if there is an accident for which the damages are less than $4000, you aren't even going to file a claim with the insurance company. The less they know, the better? You will just pay it out of pocket. You believe that any accident will result in a damage amount which is normally distributed with a mean of $4500 and a standard deviation of $1500. The value of your son's car is only $7500, so that is the upper bound on the damage amount because in that case, you can junk the car and buy a different one for $7500. The lower bound on damages is obviously $0. The probability of an automobile accident this year is 7.5%.
Build a Monte Carlo simulation model to show your out of pocket expenses in this situation. If there is no accident, then there is no out of pocket expense.
Analyze the results of the 1000 iterations to find the following as a percentage of the 1000 interactions:
1. How often a claim was filed (damage met deductible).
2. How often you ended up buying a different car.
Also, calculate your expected out of pocket expense.
For these three questions, put a cell reference in Cells B4:B6 to wherever you have calculated those values in your spreadsheet so that I don't have to hunt for them.

a. The range of WR scores that would contain about 95% of the scores in the drug dealer sample.
Given info:
The data have mount-shaped, symmetric distribution.
${\displaystyle n=100,\bar{x}=39,s=6}$.
b. The proportion of scores that lies above 51.
c. The range of WR scores that contain nearly all samples of drug dealer sample.