Let be a Gaussian random variable and let Y be a Bernoulli random variable with Pr (Y 1) and Pr (Y 1) If X and Y are independent, find the PDF of Z XY Under what conditions is a Gaussian random variable

Question: Let be a Gaussian random variable and let Y be a Bernoulli random variable with Pr (Y = 1) = and Pr (Y =1).If

Let be a Gaussian random variable and let Y be a Bernoulli random variable with Pr (Y = 1) = ρ and Pr (Y =–1).If X and Y are independent, find the PDF of Z = XY. Under what conditions is a Gaussian random variable?

Step by Step Solution

★★★★★

3.40 Rating (172 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Conditioned on Yy the transformation ZXy is a simple linear ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

589-M-S-C-R-V (1103).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Let be a Gaussian random variable such that X ~ N (0, 2). Find and plot the following conditional PDFs. (a) fx|x > 0 (x) (b) fx||x > 3 (x) (c) fx||x >3 (x)

Let X be a zero- mean, unit- variance, Gaussian random variable and let Y be a chi- square random variable with n1 degrees of freedom (see Appendix D, section D. 1.4). If X and Y are independent,...

A certain system we have designed needs to be powered by a 24- V dc supply. Available to us in our lab are each of the following types of batteries whose statistical characteristics (and quantities...

Please help! I am very confused, and I want to make sure I have done these questions properly. According to RIPTA, the 1 is supposed to arrive at the tunnel on Thayer 3 times between 1 pm and 2 pm on...

1. Consider an experiment that consists of tossing a die and flipping a coin at the same time. Define the following random variables: X1: The number of dots appearing on the die. X2: The sum of the...

Question 2: Let Y be a random variable and x be a fixed variable. Sometimes it is useful to measure the independent variable around its mean. In such a case, the model has a centered version:\...

MATH 5305: Assignment 2 Due Date: October 12, 2015 (at the start of the class) 1. A manufacturer of electronic component is interested in determining the lifetime of a certain type of battery. A...

Question 2b, please. Either by hand or using excel, but preferably by hand. 2. (10 pt each) Consider a 4-security portfolio with the following information. Expected Return Standard Deviation Stock 1...

6.1 6.2 Let y be a random variable with probability density function given by 0 y 1, = {20 elsewhere. a b f(y) = Find the density function of U = 2Y - 1. Find the density function of U = 1-2Y. C...

3. Calculate the mole fraction of benzene in solution containing 30% by mass in carbon tetrachloride.

1. It is important to recognise how to manage and control the talented employee, to invest in their skills, experience, knowledge and to enhance productivity and performance of organisations. You are...

1.1 Refer to the data and five-number summaries given in Case Study 1.1. Give a numerical value for each of the following. a. The fastest speed driven by anyone in the class. b. The slowest of the...

What are the advantages of using awards as opposed to cash as an incentive?

A quiz contains a multiple-choice question with five possible answers, only one of which is correct. Astudent plans to guess the answer because he knows absolutely nothing about the subject. a....

An investor tells you that in her estimation there is a 60% probability that the Dow Jones Industrial Averages index will increase tomorrow. a. Which approach was used to produce this figure? b....

The manager of a computer store has kept track of the number of computers sold per day. On the basis of this information, the manager produced the following list of the number of daily sales. Number...

What causes the IS curve to shift? A. A shift in the IS curve occurs when equilibrium output changes at each given real interest rate. The factors of shifting are autonomous consumption, autonomous...

The earnings of Think Company are expected to grow at an annual rate of 14% over the next 5 years and then slow to a constant rate of 10% per year. Mylanta currently pays a dividend of $0.36 per...

You paid $1 (Canadian dollar) per Liter of gas in Canada. How much money is that in American dollars per gallon? (assume $1 Canadian equals $1.05 American dollars) 500 students are polled. 400...