Using MGF s show that if X N( X , 2 X ) and Y N( Y , 2 Y ) are independent, then X Y N Y, on ti...

To show that the sum of two independent normal random variables X and Y is also a normal random vari ...

Using MGF s show that if X N( X , 2 X ) and Y

Question:

Using MGF s show that if X ∼ N(μ_X, σ²_X) and Y ∼ N(μ_Y, σ²_Y) are independent, then X + Y ~ N] + Y, on ti

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

Step by Step Answer:

Related Book For book-img-for-question

Introduction To Probability Statistics And Random Processes

ISBN: 9780990637202

1st Edition

Authors: Hossein Pishro-Nik

See More Books

Question Posted: Oct 27, 2023 02:44 AM

See More Questions

The graph of a 9th-degree polynomial with real coefficients is given below. Answer the following questions about the polynomial, by looking at its graph. Assume all real zeros here have multiplicity...
A company is considering buying a new piece of machinery that costs $ 2 0 , 0 0 0 and has a salvage value of $ 9 , 0 0 0 at the end of its 5 - year useful life. The machinery nets $ 5 , 0 0 0 per...
Show that if x is used as a point estimate of µ and s is known, the probability is 1 Î± that | µ|, the absolute value of our error, will not exceed a specified amount e when...
Two charges are located in the (x, y) plane as shown. The positive a direction is to the right and the positive y direction is upwards. The fields produced by these charges are ob- served at a point...
Is privatization a recent phenomenon? Why has it become more prominent in recent years? What triggered the move to more privatization in Latin American countries? In former communist nations?
Suppose that Head-First Company now sells both bicycle helmets and motorcycle helmets. The bicycle helmets are priced at $70 and have variable costs of $49 each. The motorcycle helmets are priced at...
LO3 What are the two basic methods of accounting that may be used by taxpayers? How do the two basic methods differ?
Everett Co. was organized on July 1, 2014. Quarterly financial statements are prepared. The unadjusted and adjusted trial balances as of September 30 are shown below. Instructions (a) Journalize the...
Question C: Analysis of Financial Statements (14 marks: 25 minutes) The condensed statement of financial position of Infotech, Inc. as at December 31, 2020 is shown below: Infotech, Inc Statement of...
Using MGFs prove that if X Binomial(m, p) and Y Binomial(n, p) are independent, then X + Y Binomial(m + n, p).
If find EX and Var(X). 1 Mx(s) = =+ =/e + 1es
Do foreign-born Americans differ from Americans born in the United States (BORN: 1 = Born in the U.S., 2 = Born elsewhere) in their support of political groups (PARTYID3: 1 = Democrat, 2 =...
1. As resistors are added in parallel to an existing circuit, what happens to the voltage drop measured across each resistor? 2. In the circuit shown on the right, which path (left or right) will...
Can anyone explain me how to calculate the ROI using the HISTORICAL COST NBV, the formula my instructor wants me to use is ADJ CF - HIST DEP /ASSETTOTAL - ACC DEP. And for the ROI of CURRENT COST NBV...
Consider the circuit to the right 3. If the total voltage supply in the circuit is 120V, and each resistor has a resistance of 400, what will the current read on each ammeter? |1= 12= 3 = 4. What...
1. The theory predicts the proportion of beans, in the four groups A, B, C and D should be 9:3:3:1. In an experiment among 1600 beans, the numbers in the four groups were 882, 313, 287 and 118. Does...
Would you recommend criminal charges in this case ( the screenshots below) and, if so, exactly which statutes against which person? Explain your reasoning (how the elements of the crime are met or...
Explain the function of an epiphyseal plate.
Q:1 Take any product or service offered in Pakistan and apply all determinents of customer Perceived value ?
Explain the meaning of the comparative performance and comparative cost data in Exhibits 18-3 and 18-4. Why does it appear that eliminating sales areas D and E would be profit able?
Most sales forecasting is subject to some error (perhaps 5 to 10 percent). Should we then expect variations in sales performance of 5 to 10 percent above or below quota? If so, how should we treat...
Why is there controversy between the advocates of the full-cost and the contribution-margin approaches to cost analysis?
estion 5 t yet answered arked out of 2 Jolly Painters provides painting services to both residential and commercial clients. In addition to paint, other materials for preparation, insurance,...
Required information Skip to question [The following information applies to the questions displayed below.] One Product Corporation (OPC) incorporated at the beginning of last year. The balances on...
Please do the Balance sheet -17 Question 6 of 6 View Policies Current Attempt in Progress Presented below are a number of balance sheet items for Marigold, Inc. for the current year, 2020. Goodwill $...

Using MGF s show that if X N( X , 2 X ) and Y

Question:

X + Y ~ N] μχ + μY, on tôi

Step by Step Answer:

To show that the sum of two independent normal random variables X and Y is also a normal random vari...View the full answer

Introduction To Probability Statistics And Random Processes

Students also viewed these Business questions