For a random variable x, a new random variable y can be created by applying a linear transformation y = a + bx, where a and b are constants. If the random variable x has mean uy and standard deviation o, then the mean, variance and standard deviation of y are given by the following formulas. Hy = a+bux oy= b°o²x oy lblox The mean annual salary for employees at a company is $36,000. At the end of the year, each employee receives a $3000 bonus and a 9% raise (based on salary). What is the new mean annual salary (including the bonus and raise) for the employees? The new mean annual salary is $

For a random variable X E(X) = 1.27, E(X²) = 3.79 The variance of X is equal to Select one: O 2.52 O 2.9843 O 2.1771 O 0.758 0.3351

Let G and H be two independent unbiased estimators of 0. Assume that the variance of G is two times the variance of H. Find the constants a andb so that aG + bH is an unbiased estimator with the smallest possible variance for such a linear combination.

Psi is a measure of compressive strength, or the ability of the material to carry loads and handle compression. The desired concrete psi rating used for sidewalks and residential driveways ranges from 2500psi to 3000psi obtained from mixing cement, stone, and sand in different ratios but with the same amount of water. The summary of the psi's of three (3) such concrete mixes made by three (3) different civil engineering students is given as follows: Mean vector: The variance-covariance matrix: Concrete mix Mean Concrete mix 1 Concrete mix 2 Concrete mix 3 Concrete mix 1 | Concrete mix 2 2700 18 12 2 3000 12 16 3 2400 Concrete mix 3 16 25 Let the random variable Y be the vector of the psi's of concrete mixes obtained by the students, i.e. Y1, denotes the psi of concrete mix made by student 1, Y2 is the psi of concrete mix made by student 2 and Y3 is the psi of concrete mix psi made by student 3. (a) Find (i) the multivariate probability distribution function (pdf) of Y. (ii) the…

4. As fallen trees lie on the forest floor they slowly decay. Will the amount of light present have an impact on the rate of decay? In the following table x is a random variable representing the remaining percentage of total mass of a log after it was exposed to the elements for three weeks while y represents the numbers of hours of direct sunlight the log received each day. X 0.60 .70 .65 .82 .87 y 1.0 2.3 3.0 4.0 4.5 (a) Plot a scatter diagram of the data. Remember to label your axes appropriately and choose a consistent scale. (b) Based on a scatter diagram, would you estimate the correlation coefficient to be positive, close to zero, or negative? Please circle one of the following choices: A. Positive B. Close to zero C. Negative (c) Interpret your results from parts (a) and (b). 16 tv

Consider an MA(2) model: STEPS -Write the equation of the M(2) model-Determine the model based on the delay operator.- Find the expected value of the model- Find the variance of the model.- Find the covariances associated with 1,2, and s steps.- Find the associated correlation indices of 1,2, and s steps.- Assume that information is available up to time $h$ and the function that contains the accumulated information f(h, h-1,……), determine the forecasts and the error associated with 1,2, and s steps.