Question: Suppose that Xi has a normal distribution with mean i and variance i 2 , i = 1, 2. Let X1 and X2 be independent.

Suppose that Xi has a normal distribution with mean μi and variance σi 2 , i = 1, 2. Let X1 and X2 be independent.
(a) Find the moment-generating function of Y = X1 + X1.
(b) What is the distribution of the random variable Y?

Step by Step Solution

★★★★★

3.50 Rating (173 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a b is the momentgenerating function of a normal ... 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

Students Have Also Explored These Related Applied Statistics and Probability Questions!

The Cell Tone Company sells cellular phones and airtime in several northwestern states. At a recent meeting, the marketing manager stated that the average age of its customers is under 40. This came...

If x has a normal distribution with mean = 15 and standard deviation = 3, describe the distribution of values for sample size n, where n = 4, n = 16, and n = 100. How do the x distributions compare...

Suppose x has a normal distribution with = 1.2. (a) Find the minimal sample size required so that for a 90% confidence interval, the maximal margin of error is E = 0.5. (b) Based on this sample size...

A. Sivathayalan, M. Nasari, Z. Montazeri STAT 2507 Assignment # 3 (Chapters 6, 7 and 8) Due: Tuesday, March 22, 2016, in class Last Name Student # Tarannum First Name 100838870 Your LAB Section...

2. Normal Sample Mean and Sample Variance, Part 1 Let X1, X2, , Xn be i.i.d. with mean u and variance 0'2. Let denote the sample mean. In Homework 9, you constructed a random variable 52: 1 ion X?...

STAT 2507 H Assignment # 2 (Chapters 4, 5, and 6) Due: Monday, March 2, 2015, in class Last Name First Name - Student # LAB Section - Note: Use spaces left to answer all questions. The total of marks...

Thx for helping (4 pt) Let X1, X2, Xn be nindependently and identically distributed random variables with mean p, and variance 0? . While we have learned in class that by the Central Limit Theorem...

Suppose that X1 and X2 are independent random variables, and that Xi has the normal distribution with mean bi and variance 2i for i = 1, 2. Suppose also that b1, b2, 21, and 22 are known positive...

Answer the questions 1 An insurer is setting the premium rate for the buildings in an industrial estate. Past experience fo the estate indicates that a premium rate of f3 per f1,000 sum insured...

Let X be a random variable with mean and variance 2, and let X1, X2,., Xn be a random sample of a continuous random variable with cumulative distribution function F(x). Find E[F(X(n))] and E[F(X(1))].

The rate of movement (flux) of a substance X into cells was measured at different concentrations of X to construct the following graph. (a) Does this information suggest that the movement of X into...

The Charter Company's total assets are equal to $700,000 and its equity is $420,000. What is the amount of your debts? B. Martin Marine's total assets are equal to $500,000 and its liabilities and...

2. Which of the following is most indicative of a decentralized organization? a. The physical facilities of the company are widely dispersed geographically. b. The organization is divided into...

1 What is wrong with this statement: How much money did you make last year?

Test this correlation for statistical significance, and report a p-value? Cancer The following statistics are taken from an article by Burch relating cigarette smoking to lung cancer [13]. The...

Fit a regression line relating 5-year lung-cancer mortality to annual cigarette consumption when each is expressed in the log 10 scale? Cancer The following statistics are taken from an article by...

To test the significance of this regression line, is it necessary to perform any additional tests other than those in Problem 11.20? If so, perform them. Cancer The following statistics are taken...

Bond P is a premium bond with an 7.4 percent coupon, a YTM of 6.15 percent, and 15 years to maturity. Bond D is a discount bond with an 7.4 percent coupon, a YTM of 9.15 percent, and also 15 years to...

Teeswater Corp. shows the following information on its 2 0 2 0 statement of comprehensive income: sales = $ 2 4 2 , 0 0 0 ; costs = $ 1 4 6 , 0 0 0 ; other expenses = $ 8 , 4 0 0 ; depreciation...

Using Rstudio We will use a logistic regression to predict the probability ofdefaultusing income andbalanceon theDefaultdata set in the ISLR package. We will now estimate the test error of this...