Let X X 1 X 2 T denote a bivariate normal (Gaussian) random vector Assume and Define Y l X 1 X 2 and Y2 X 1 X 2 1 Find the joint distribution of Y 1 and Y 2 find the marginal distributions of Y l and Y2 2 Find the conditional density of X l , given Y l find the conditional density of X l , given Y2...

Here in this given problem X 1 X 2 2 BN 0 0 1 1 e From properties of BN we know any l ...

Let X = [X 1 X 2 ] T denote a bivariate normal. (Gaussian) random vector. Assume

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

Question:

Let X = [X ₁ X ₂] ^T denote a bivariate normal. (Gaussian) random vector. Assume

and

Define Y _l = X ₁+ X ₂and Y2 = -X ₁ + X ₂

1. Find the joint distribution of Y ₁ and Y ₂; find the marginal distributions of Y _l and Y2.

2. Find the conditional density of X _l, given Y _l; find the conditional density of X _l, given Y2.

3. Find the conditional mean and variance of X ₁, given Y _l; find the conditional mean and variance of X _l, given Y ₂.

Related Book For answer-question

Modeling the Dynamics of Life Calculus and Probability for Life Scientists

ISBN: 978-0840064189

3rd edition

Authors: Frederick R. Adler

See More Books

Posted Date: Nov 29, 2018 01:16 AM

See More Questions

The joint distribution of the continuous random variables X, Y, and Z is constant over the region (a) Determine P(X2 + Y2 < 0.5) (b) Determine P(X2 + Y2 < 0.5, Z < 2) (c) What is the joint...
Find the joint distribution if immigrants enter the two populations independently. Suppose immigration and emigration change the sizes of two populations with the following probabilities. Let Ia...
The joint distribution of the continuous random variables X, Y, and Z is constant over the region x 2 + y 2 1, 0 < z < 4. Determine the following: (a) P(X 2 + Y 2 0.5) (b) P(X 2 + Y 2 0.5, Z <2)...
The adjusted trial balances of Rosa Corporation at August 31, 2014, and August 31, 2013, include these amounts (in millions): Rosa completed these transactions (in millions) during the year ended...
Show how you would synthesize each compound from starting materials containing no more than six carbon atoms. (a) (b) (c) CH2CH CHC CH
How could you synthesize isopropyl propyl ether, using isopropyl alcohol as the only carbon-containing reagent?
Review the California form interrogatories for particular civil cases at www.courts.ca.gov/formsrules.htm. Are these questions helpful in developing your own set of interrogatories in a case?
Cooperative enterprises are collectively owned, and their affairs are directed through shared governance. Use the preceding theory to discuss the management of some cooperative enterprises with which...
At December 31 Assets Cash Accounts receivable, net Inventory MONTGOMERY INCORPORATED Comparative Balance Sheets Current Year Prior Year $ 56,900 14,100 126,400 197,400 70,000 (31,700) $ 57,100...
A child appears to be suffering from I-cell disease, but when a sample of his proteins (lane 3* below), isolated from skin fibroblasts, is compared to protein samples from fibroblasts of his healthy...
Write a short informative speech, using any one of the following speech types: (1) Explanation, (2) report, (3) description, or (4) demonstration
The non-controlling (minority) interest in consolidated subsidiaries is presented on the balance sheet: A. as a long-term liability. B. separately, but as a part of shareholders equity. C. as a...
An analyst is evaluating the solvency and liquidity of Apex Manufacturing and has collected the following data (in millions of euro): Which of the following would be the analysts most likely...
Which is an appropriate method of preparing a common-size cash flow statement? A. Show each item of revenue and expense as a percentage of net revenue. B. Show each line item on the cash flow...
Cash flows from taxes on income must be separately disclosed under: A. IFRS only. B. US GAAP only. C. both IFRS and US GAAP.
An analyst gathered the following information from a companys 2010 financial statements (in $ millions): In 2010, the company declared and paid cash dividends of $10 million and recorded depreciation...
You are a Levi's sales executive, You will be meeting with the owner of Jesse's Jeans. Your primary objective is to obtain an order for 100 of the specialty jean jackets. Read the case and complete...
A bar of a steel alloy that exhibits the stress-strain behavior shown in Figure 6.22 is subjected to a tensile load; the specimen is 375 mm (14.8 in.) long and has a square cross section 5.5 mm (0.22...
Annual savings stream of $429.59 invested for 50 years at 10% a year would satisfy a savings goal of $500,000. Suppose instead that you made 50 annual investments, but you made these investments at...
Bird D from Exercise 22. Find the correlation of the number of lice and mites for the above bird. Bird C Lice Bird D Lice 0 0.21 0.13 0.16 0.06 021 0.23 Mites 0.13 0.07 0.10 0.21 0.03 0.06 2 006 0.10...
In a repeated experiment, the cell in the salubrious bath survives 60 min, and a cell in standard culture survives only 3 min. Is there reason to think that the salubrious bath lengthens cell life?...
Suppose that n = 50 and that Xi takes the value 0 with probability 0.25, the value 1 with probability 0.5, and the value 2 with probability 0.25. Compare with the results in Exercise 2. The Central...
Ski resorts are interested in the mean age that children take their first ski and snowboard lessons. They need this information to plan their ski classes optimally. identify: a. the population, b....
Insurance companies are interested in the mean health costs each year of their clients, so that they can determine the costs of health insurance. identify: a. the population, b. the sample, c. the...
A fitness center is interested in the mean amount of time a client exercises in the center each week. identify: a. the population, b. the sample, c. the parameter, d. the statistic, e. the variable,...

Let X = [X 1 X 2 ] T denote a bivariate normal. (Gaussian) random vector. Assume

Question:

EX = 0 EXXT = [1]. EX = 0 EXXT = [1].

Expert Answer:

Here in this given problem X 1 X 2 2 BN 0 0 1 1 e From properties of BN we know any l... View the full answer

Modeling the Dynamics of Life Calculus and Probability for Life Scientists

Students also viewed these mathematics questions