### Independent Random Variables, Mean, Variance and Conditional Density

Please see the attached file for the fully formatted problems. keywords: rv r.v. irv i.r.v.

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Please see the attached file for the fully formatted problems. keywords: rv r.v. irv i.r.v.

You're conducting a study where participants are randomly assigned to two independent variables: number of sessions of psychotherapy (6 vs. 12) and use of antidepressants (using vs. not) on psychotherapy outcome. You would be pretty happy if you were checking assumptions for your ANOVA test and found this result. A. Levene

What is ANOVA and how is it used?

Overview River Beverages is a food and soft-drink company with worldwide operations. The company is organized into five regional divisions with each vice president reporting directly to the CEO, Cindy Wilkins. Each vice president has an R&D department, controller, and three divisions; carbonated drinks, juices and water, and f

An instructor asked 5 students how many hours they had studied for an exam. Here are the hours and the students grades Hours Grade 0 52 10 95 6 83 8 71 6 64 a. make a scatter diagram of the raw scores b. describe in words the general pattern of association c. figure the correlation coefficient d. explain

X and Y are random variables. What are the marginal pdfs of (x+y) (where 0<x<1 and 0<y<1)? What is the expectation, covariance, correlation and and covariance coefficient? What are the joint and marginal pdfs and cdfs? (ii) Also,differently - if Fx|y(x|y) is constant over the 0 to 1. What is Fy|x(y|x)? (is there enough

At the end of 2003, Al Second, vice president of Chicago Syndicate, Inc., stared out the window of his posh west side office in dismay. His expectations for a highly profitable year were dashed. The disappointing results appear below: Mr. Second realized that because sales were down, expenses should also fall, such that pr

Compute the Mean and Variance of a Uniform Continuous Random variable on the interval [a, b].

I need some help with this statistics problem as well as some help understanding limiting distribution and the limiting extreme-value distribution: Consider a random sample of size n from a distribution with CDF (cumulative distribution function) F(x)=1-1/x if , and zero otherwise. a) Derive the CDF of the smallest order sta

1) What has been the expected return and risk for the S&P 500 during that time period (average annual return and standard deviation)? 2) How does the portfolio fair compare to the S&P 500? Explain. 3) Your client has $50,000 to invest and you plan to invest 60% in the security with the highest expected return. What would b

Risk and Return. True or false? Explain or qualify as necessary. a. The expected rate of return on an investment with a beta of 2 is twice as high as the expected rate of return of the market portfolio. b. The contribution of a stock to the risk of a diversified portfolio depends on the market risk

Let Y the sum of a random sample of n=192 uniform random variables on the interval (0,1). Use a normal approximation to find P(Y>100).

Find the variance of the random variable Y, where the pdf of Y is given by f(y) = 3(1 - y)^2, 0 < y < 1.

Hours Studied...........Test Grade ........0..............................52 .......10.............................95 ........6..............................83 ........8..............................71 ........6..............................64 Give the proportion of variance accounted for (R2).

Q1. For the set of numbers given: 9, 8, 7, 27, 16, 3, 1, 9, 4 and 16 determine: (a) the mean (b) the median (c) the mode (d) the variance from the mean and from it calculate the standard deviation. All calculations must be shown for (a), (b) and (c) and a hand drawn table consisting of manipulated data elements and calculati

If we do not observe a sufficiently large between-groups variance, then we have not observed __________ experimenter effects, an effect of the dependent variable, enough samples, or an effect of the independent variable I believe - enough samples - is the answer.

Verify that Var(X) =α/λ² when X is a gamma random variable with paramaters α and λ.

4.17. X has the U(?pi/2, pi/2) distribution, and Y = tan(X). Show that V has density l/(pi(1 + y2)) for ?oo <y <oo . (This is the Cauchy density function.) What can be said about the mean and variance of Y? How could you simulate values from this distribution, given a supply of U(O, 1) values? 4.21. Let X and Y have joint den

Let X be a random variable having expected value (mu) and variance (sigma)^2. Find the expected value and variance of: Y = (X - mu)/(sigma). (See attachment for full question)

1. Suppose U is a uniformly distributed random variable, so it has density fU(u) = 1 for 0u1, fU(u) otherwise. Calculate the expected values E[U] and E[U 2], and the variance of U. (Please see attachment.)

I need to measure the convergence of annual provincial data relative to the national. I have data for per capita annual income for two provinces and I have to compare them with the per capita national data and evaluate if the provincial data converge toward the national data. Can I do this with variance or standard deviation?

Suppose the error variance in your study is high. Which of these statements is most likely to be true? a. Your power is high. b. The relationship between your independent variable and dependent variance is strong. c. Confounds interfered with measuring your dependent variable or manipulating your independent variable.

A. Which of the models would you use to determine the best choice of expiration date for the green beans? The cream pie? Why would you choose these? b. If, for practical reasons, you had to choose only one model to use to set the expiration dates, which would it be? (There is no health risk involved. It's a flavor quality thing

Let X and Y be independent random variables with mean j and k and variances m^2 and n^2. Find an expression for the correlation of XY and Y in terms of these means and variances.

Please see the attached file for full problem description. --- ? A random sample of independent observations is taken from a Rayleigh distribution, whose density function is given by for x> or equal to 0 0 if x<0 show that the maximum likelihood estimate is given by . Using the result that deduce that is

Wage negotiations between your firm and the union representing your workers are about to collapse. There is considerable disagreement about the mean wage level of workers in Plant A and in Plant B. Wages wee set by the old labor agreement reached three years ago and are based strictly on seniority. Although wages are closely con

Show that standard error of the estimate (SEest)= the standard deviation of variable Y when the correlation is 0.

An urn contains four red balls and four white balls. An experiment consists of selecting at random a sample of four balls and recording the number of red balls in the sample. Set up the probability distribution and compute its mean and variance.

Student A received the following course grades during her first year of college: 4, 4, 4, 4, 3, 3, 2, 2, 2, 2, 0. Student B received the following grades during her first year of college: 4, 4, 4, 4, 4, 4, 3, 1, 1, 1. (a) Write down the relative frequency distribution tables for each student, and compute the population mea

Two golfers recorded their scores for 20 nine-hole rounds of golf. Golfer A's scores were: 39, 39, 40, 40, 40, 40, 40, 40, 41, 41, 41, 41, 41, 41, 41, 42, 43, 43, 43, 44. Golfer B's Scores were: 40, 40, 40, 41, 41, 41, 41, 42, 42, 42, 42, 42, 43, 43, 43, 43, 43, 43, 44, 44. (a) Compute the sample mean and the variance of ea