Reference no: EM131216266
Q1. Let x ∼ Nk (0, σ2I) and let y = px, where P is a k x k orthogonal matrix. Show that y has a Nk (0, σ2I) distribution.
Q2. Suppose Y ∼ N3 (0, I3).
(a) Show that Q = 1/3[(Yl - Y2)2 + (Y2 - Y3)2 + (Y3 - Y1)2] has a χ2(2) distribution.
(b) Find the distribution of
. What can you tell about the density of V?
Q3. Let Z ∼ N3(0, I3)and Y = µ + AZ, where
(a) Use R to find the mean and variance of Ymax = max{Y1, Y2, Y3, Y4} by simulation.
(b) Simulate 10000 values of (Y - µ)'∑-(Y - µ), where ∑- is a g-inverse for the covariance of Y. Find the mean and variance of the simulated values. Also draw the histogram and the density of the simulated values.
|
Using the multiplier effect and behavioral explanation
: In recent years Sweep Programs have grown throughout the U.S. With this financial innovation, banks automatically sweep excess funds from their customers’ checkable deposits into interest bearing MMDAs, which are part of savings and time deposits. Us..
|
|
Approximate probability that class average falls below 75
: If there are 100 students in the class, use the central limit theorem to approximate the probability that the class average falls below 75.
|
|
Use the codification to identify accounting authority
: Use the Codification to identify accounting authority (location within the Codification) governing each of the following:
|
|
Discuss the purpose and philosophical approach
: For additional information on completing your AnnotatedBibliography, you may want to review a webinar on the topic by clicking on thefollowing link:Literature Review and Annotated Bibliography Basics Webinar.
|
|
Draw the histogram and the density of the simulated values
: Simulate 10000 values of (Y - µ)'∑-(Y - µ), where ∑- is a g-inverse for the covariance of Y. Find the mean and variance of the simulated values. Also draw the histogram and the density of the simulated values
|
|
Find a bound to the probability using markovs inequality
: Find a bound to the probability using Markov's inequality. - Find a bound to the probability using Chebyshev's inequality.
|
|
Calculate the payback period for each of the investments
: Calculate the payback period for each of the investments. If the maximum acceptable payback period is 3 years, which of the investments would be accepted?
|
|
Do you perceive an ethical dilemma
: You are in your second year as an auditor with Dantly and Regis, a regional CPA firm. One of the firm's long-time clients is Mayberry-Cleaver Industries, a national company involved in the manufacturing, marketing, and sales of hydraulic devices used..
|
|
How many time do we need to run the experiment
: How large does need to be? In other words, how many time do we need to run the experiment?- find an expression for the average number of times the event is observed.
|