Presidential stature
In a race for U.S. president, is the taller candidate more likely to win?
1.4.28 In the first election of the 20th century, Theodore Roosevelt (178 cm) defeated Alton B. Parker (175 cm). There have been 27 additional elections since then, for a total of 28. Of these, 25 elections had only two major party candidates with one taller than the other. In 19 of the 25 elections, the taller candidate won.
a. Let π = P(taller wins). State the research hypothesis in words and in symbols.
b. State the null and alternative hypotheses in words and symbols.
c. Compute the appropriate p-value using an applet.
d. If you take the p-value at face value, what do you
conclude?
e. Are there reasons not to take the p-value at face value? Is yes, list them

Suppose you are dealt 5 random cards from a standard deck of 52 cards, where all cards are equally likely to appear.

(a) What is your outcome space?

(b) What is the probability that you receive the ace of hearts?

(c) Let AH be the event that you receive the ace of hearts, AC the event that you receive the ace of clubs, AD the event that you receive the ace of diamonds, and AS the event that you receive the ace of spades. If A is the event that you receive at least one ace, write A in terms of AH, AC, AD, and AS.

(d) Use the union bound to give an upper bound on the probability of A.

Match the following statistical tests with the level of measurement or other requirement required for each analysis.

Pearson r

      [ Choose ]            Ordinal, very small group size            Interval or ratio data            Ordinal data            Nominal data      

Spearman 's Rank Order (rho)

      [ Choose ]            Ordinal, very small group size            Interval or ratio data            Ordinal data            Nominal data      

Kendall's Tau

      [ Choose ]            Ordinal, very small group size            Interval or ratio data            Ordinal data            Nominal data      

Chi Square

      [ Choose ]            Ordinal, very small group size            Interval or ratio data            Ordinal data            Nominal data      

The following table shows the annual returns (in percent) and summary measures for a sample of returns from the Vanguard Energy Fund and the Vanguard Health Care Fund from 2012 through 2016.

If the risk-free rate is 3%, using mean-variance analysis, which fund performed better, and why?

An experiment consists of rolling 1 red die, 1 white die, and 1 blue die and noting the result of each roll. The dice are fair, and all out comes are equally likely,

What is the probability that the SUM of the results on the three dice is 7?

What is the probability that the sum is an odd number?

Please explain in detail.  

The random variable X, which denotes the interval between two consecutive events, has the PDF: fx (?) = 4?^( 2)?^( −2?) ? ≥ 0 If we assume that intervals between events are independent, determine the following: (a) The expected value of X. (b) The expected value of the interval between the 11th and 13th events (c) The probability that ? ≤ 6.

1. CPK and SGOT tests are used in the diagnosis of myocardial infarction (MI). When the CPK test is given to a patient who does not have a MI, the probability of a negative finding (i.e. its specificity) is 0.6. The probability that the SGOT test will be negative for a non-MI patient is 0.7. When both tests are given to a non-MI patient the probability that at least one is negative is 0.9. For a non-MI patient who has both tests:

1. What is the probability that both tests are negative?
2. What is the probability that both tests are positive?

Hints: (1) Answer is not 0.12 -- tests are not to be assumed to be independent.

           (2) Using 2-by-2 table to structure your calculations can help.

3. What is the probability that at least one test is positive?

The accompanying data set provides the closing prices for four stocks and the stock exchange over 12 days:

Using Excel's Data Analysis Exponential Smoothing tool, forecast each of the stock prices using simple exponential smoothing with a smoothing constant of 0.3.

For example, help me to understand how to complete the exponential smoothing forecast model for Stock A.

Date Forecast A

9/3/2010 ____

9/7/2010 ____

9/8/2010 ____

9/9/2010 ____

9/10/2010 ____

9/13/2010 ____

9/14/2010 ____

9/15/2010 ____

9/16/2010 ____

9/17/2010 ____

9/20/2010 ____

9/21/2010 ____

In a political science class there are 15 political science majors and 9 non-political science majors. 4 students are randomly selected to present a topic. What is the probability that at least 2 of the 4 students selected are political science majors? Express your answer as a fraction or a decimal number rounded to four decimal places.

if two people are randomly selected from a class of 30 students, what is the probability that they have the same birthday?

Give the expected value, variance, and probability distribution for the sum of a fair coin and a random real number chosen uniformly in the range [ -1, 1]. Sketch the PMF.

Problem 4: Suppose M is a random matrix, and x is a deterministic (fixed) column vector. Show that E[x' M x] = x' E[M] x, where x' denotes the transpose of x.

In the binomial function, negative binomial function, poisson distribution, I dont know what to do when we need to find a variable X. For example, If X is exactly at 0, 1 , 2, etc. Then I know that we only need to apply the formula and calculate it. However, in some cases like X <= 2, X >= 5, X > 4, etc, then I do not know how to calculate that X and how to apply the formula. Ex: If P( X >= 4) = 1 - P(X <= 3) and for X <= 3, we will calculate the sum of X = 0, X = 1, X = 2, X = 3. How to define when to use 1 - P(X <= 3) or how P(X = 4) = P(X <= 4) - P(X <= 3). It really hard for me to understand this concept. Is there any formula or any way to define it so you know when to subtract, or when to add it together? Thank you.

While the housing market was in recession and was not likely to emerge anytime soon, real estate investment in college towns continued to promise good returns (The Wall Street Journal, September 24, 2010). Michele Gibellino worked for an investment firm in Michigan. Her assignment was to analyze the rental market in Ann Arbor, which is home to the University of Michigan. She gathered data on monthly rent for 2011 for a sample of 40 homes. The data is shown in the accompanying table.

Monthly Rent Monthly Rent Monthly Rent Monthly Rent

645 905 1084 1518

675 929 1100 1600

760 960 1100 1635

800 975 1185 1635

820 990 1245 1650

850 995 1275 1750

855 1029 1275 1950

859 1039 1400 1975

900 1049 1450 2200

905 1050 1500 2400

Tell me about the monthly rents. Choose the appropriate description.

Please show all work and all steps.

1.) Two cards are drawn from a standard 52-card playing deck. What is the probability that the draw will yield an ace and a face card?

2.) Articles coming through an inspection line are visually inspected by two successive inspectors. When a defective article comes through the inspection line, the probability that it gets by the first inspector is .1. The second inspector will "miss" five out of ten of the defective items that get past the first inspector. What is the probability that a defective item gets by both inspectors?

3.) A diagnostic test for a disease is such that it (correctly) detects the disease in 90% of the individuals who actually have the disease. Also, if a person does not have the disease, the test will report that he or she does not have it with probability .9. Only 1% of the population has the disease in question. If a person is chosen at random from the population and the diagnostic test indicates that she has the disease, what is the conditional probability that she does, in fact, have the disease? Are you surprised by the answer? Would you call this diagnostic test reliable?