If n independent random variables Xi have normal distributions with the means i and the standard deviations i, find the moment generating function of their sum and identify the corresponding distribution, its mean, and its variance ...

If n independent random variables Xi have normal distributions with the means i and the standard deviations

Question:

If n independent random variables Xi have normal distributions with the means µi and the standard deviations σi, find the moment-generating function of their sum and identify the corresponding distribution, its mean, and its variance.

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

Step by Step Answer:

Related Book For book-img-for-question

John E Freunds Mathematical Statistics With Applications

ISBN: 9780134995373

8th Edition

Authors: Irwin Miller, Marylees Miller

See More Books

Question Posted: Nov 04, 2015 03:23 AM

See More Questions

Use the result of Exercise 7.45 to show that, if n independent random variables Xi have normal distributions with the means i and the standard deviations i, then Y = 1X1 + 2X2 + + anXn has a...
The following is a sufficient condition for the central limit theorem: If the random variables X1, X2, . . . , Xn are independent and uniformly bounded (that is, there exists a positive constant k...
If n independent random variables have the same gamma distribution with the parameters and , find the moment-generating function of their sum and, if possible, identify its distribution.
Julie is the insured on a $300,000 ordinary life insurance policy. Julie sells her life insurance policy to Ben for $20,000. Ben promptly named himself beneficiary. The policy had a cash surrender...
a. Find the area under the normal curve for z between z(0.95) and z(0.025). b. Find z(0.025) - z(0.95).
Presented below is the December 31 trial balance of New York Boutique. Instructions(a) Construct T-accounts and enter the balances shown.(b) Prepare adjusting journal entries for the following and...
Von Krmn assumed a cubic profile for the integral momentum analysis over a flat plate. Since a cubic has four constants, four conditions were used. (i) $V_{x}=0$ at $y=0$. (ii)...
Martial Arts R Us (MARU) needs a database. MARU is a martial arts school with hundreds of students. It is necessary to keep track of all the different classes that are being offered, who is assigned...
Directions: Prepare general journal entries on December 31 to record the following year-end adjustments. a. Estimated depreciation on office equipment for the year, $4,000. b. The Prepaid Insurance...
When Brittany purchased a new battery for her SUV, she paid 7% sales tax plus a $5 battery recycling fee. If the total cost Brittany paid was $208.30, determine the cost of the battery before the...
Find the moment-generating function of the negative binomial distribution by making use of the fact that if k independent random variables have geometric distributions with the same parameter , their...
Prove the following generalization of Theorem 7.3: If X1, X2, . . ., and Xn are independent random variables and Y = a1X1 + a2X2 + · · · + anXn, then Where MXi(t) is the value of...
The balances for the accounts listed below appear in the Adjusted Trial Balance columns of the end-of-period spreadsheet. Indicate whether each account would flow into the income statement, statement...
When two people turn away from each other, without further discussion or dialogue after they had a dispute, it is said to be Ulterior transactions Complementary transactions Crossed transactions. ...
Who are the victims of workplace violence? What are the warning signs for workplace violence?
How is the psychopath different from the nonpsychopath on psychophysiology? Thoroughly discuss all relevant features.
Crossed transactions are not a source of conflict. True False
List and define the types of multiple murder, and provide an illustration of each.
Evaluate the function for the indicated inputs and interpret the result. A(5,8), where A(b, h) = 1/2bh (A computes the area of a triangle with base b and height h.)
Juarez worked for Westarz Homes at construction sites for five years. Bever was a superintendent at construction sites, supervising subcontractors and moving trash from sites to landfills. He...
A family has eight children. If this family has exactly three boys, how many different birth and gender orders are possible?
In the Illinois Lottery game Little Lotto, an urn contains balls numbered 1 to 39. From this urn, 5 balls are chosen randomly, without replacement. For a $1 bet, a player chooses one set of ve...
In Mega Millions, an urn contains balls numbered 1 to 56, and a second urn contains balls numbered 1 to 46. From the rst urn, 5 balls are chosen randomly, without replacement and without regard to...
1) Pretend that you work in a hospital. Its not really possible to have an MVP for something like surgery. For example, you cant complete half a surgery, check for market feedback, then go back and...
Many Geotechnical engineering projects require knowledge of the shear strength of soils. What is the purpose and goal of the direct shear test ?
a) A person has set out to deposit $750 per month for 5 years (60 months) into a bank account that pays 1.75% per month interest at the end of each month. What will be the accumulated amount at the...

If n independent random variables Xi have normal distributions with the means i and the standard deviations

Question:

Step by Step Answer:

M X e t12t22 Y is a r...View the full answer

John E Freunds Mathematical Statistics With Applications

Students also viewed these Statistics questions