X and Z are independent random variables with E[X] = E[Z] = 0 and variance Var [X]

Question:

X and Z are independent random variables with E[X] = E[Z] = 0 and variance Var [X] = 1 and Var [Z] = 16. Let Y = X + Z. Find the correlation coefficient p of x and Y, Are X and Y independent?

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Probability and Stochastic Processes A Friendly Introduction for Electrical and Computer Engineers

ISBN: 978-1118324561

3rd edition

Authors: Roy D. Yates, David J. Goodman

See More Books

Question Posted: Jul 18, 2016 08:41 AM

See More Questions

If X, Y, and Z are independent random variables having identical density functions f(x) = ex, 0 < x < , derive the joint distribution of U = X + Y, V = X + Z, W = Y + Z.
Suppose X, Y, and Z are independent random variables that take values 1 and 2 with probability 1/2 each. Find the pmf of (X, Y,Z).
If X and Y are independent random variables with variances 2x = 5 and at = 3, find the variance of the random variable Z = 2X + 4Y 3.
The crate has a mass of 80 kg and is being towed by a chain which is always directed at 20 degrees from the horizontal. If the magnitude of P is increased until the crate begins to slide, determine...
How can you measure and take into account differences among workers in terms of their development needs and interests?
Acme Storage is evaluating an investment to produce a new product with an extended marketable life of 4 years. In order to produce this product, the company will have to acquire a piece of new...
14. Calculate the ES, EF, LS, and LF times and the slack for each activity in the figure below, and identify the critical path for the project. Can the project be completed in 30 weeks? Assume that...
Flaherty Accounting Services pays $2,000 per month for a tax software license. In addition, variable charges incurred average $9 for every tax return the firm prepares. a. Determine the total cost...
13 14 15 16 QUESTION 6 Fatima celebrates each year the accomplishments of her employees by having an organised function dinner where she hands out recognition awards. This is an example of financial...
A randomized controlled trial comparing two drugs for treating insomnia is said to have 85% power to detect a 20% relative reduction (RR=0.80) in sleep problems nine months following treatment at the...
X and Y are identically distributed random variables with E[X] = E[Y] = 0 and convariance Cov [X,Y] = 3 and correlation Px,y =1/2. For nonzero constants a and b, U = aX and V = bY. (a) Find Cov[U,v]....
For the random variable X and Y in Problem 5.2.2 find (a) The expected value of W = 2xy (b) The Correlation, rx,y = E[XY], (c) The covariance, Cov[X,Y], (d) The correlation coefficient, P X,Y (e) the...
Show that the equation has exactly one real root. x 3 + e x = 0
Explain in details the reasons for your classifications. Classify the following processes as batch, continuous, or semibatch, and transient or steady- state. 1. A balloon is filled with air at a...
Question 5. A first responder drone of mass m slug is launched with a velocity vo ft/sec and constant engine force F from a level ground and moves vertically upward to discover a sense of life in a...
As part of the investigation of the collapse of the roof of a building. a testing laboratory is given all the available bolts that connected the steel structure at 3 different positions on the roof....
1) Baris Diary Co. has three product and divisions for production process of Milk, Yogurt and Cheese. Company's data show following resulst for 2014: Milk Yogurt Revenue 100.000TL 125.000TL Cheese...
Problem 11-4B (Algo) Prepare a statement of cash flows-indirect method (LO11-2, 11-3, 11-4, 11-5) The income statement, balance sheets, and additional information for Virtual Gaming Systems are...
Use the rejection method to generate a random variable having density function Beta(2; 4). Assume g(x) = 1 for 0 < x < 1.
You are the newly appointed tax practitioner to complete Emilys tax return and have downloaded the prefill report for Emilys tax return (hint, you can read what a prefill report is here (Links to an...
Consider the situation of Example 2.31. (a) What is the probability that no more than 4 cars will be serviced by the mechanic? (b) What is the probability that he will service fewer than 8 cars? (c)...
Interest centers around the nature of an oven purchased at a particular department store. It can be either a gas or electric oven. Consider the decision made by six distinct customers. (a) Suppose...
It is common in many industrial areas to use a filling machine to fill boxes full of product. This occurs in the food industry as well as other areas in which the product is used in the home, for...
Cost of debt with fees . Kenny Enterprises will issue a bond with a par value of $1,000, a maturity of twenty years, and a coupon rate of 9.9% with semiannual payments, and will use an investment...
Assume that an investment of $100,000 is expected to grow during the next year by 8% with SD 20%, and that the return is normally distributed. Whats the 5% VaR for the investment? A. $24,898 B....
Simpson Ltd is a small IT company, which has 2 million shares outstanding and a share price of $20 per share. The management of Simpson plans to increase debt and suggests it will generate $3 million...

X and Z are independent random variables with E[X] = E[Z] = 0 and variance Var [X]

Question:

Step by Step Answer:

Independence of X and Z implies VarY VarX VarZ 12 42 17 1 Since EX EY 0 t...View the full answer

Probability and Stochastic Processes A Friendly Introduction for Electrical and Computer Engineers

Students also viewed these Statistics questions