Let X1, , Xn be a random sample, each with mean m1 and standard deviation s1 Also, let Y1, Y2, , Ym be a random sample, each with mean 2 and a standard deviation 2 Assume that both the samples are from normal populations Verify that (X Y) N(H1 42 o )

Question: Let X1, . . ., Xn be a random sample, each with mean m1 and standard deviation s1. Also, let Y1, Y2, . . .,

Let X1, . . ., Xn be a random sample, each with mean m1 and standard deviation s1. Also, let Y1, Y2, . . ., Ym be a random sample, each with mean Î¼2 and a standard deviation Ïƒ2. Assume that both the samples are from normal populations. Verify that

(X Y) ~N(H1-42.o +).

Step by Step Solution

★★★★★

3.34 Rating (157 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

for then for then ... 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

Document Format (1 attachment)

610-M-S-S-D (2219).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Let X1, . . ., Xn be a random sample from a G(1, ) distribution. (a) Show that is a sufficient statistic for . (b) The following is a random sample from a G (1, ) distribution. Find a sufficient...

Let X1,..., Xn be a random sample, where X- and S2 are calculated in the usual way (a) Assume now that the X,s have a finite fourth moment, and denote 6 = EX*, 02 - E(xi-e1y,j = 2,3,4 (b)Show that...

Let X1, . . . , Xn be a random sample from the exponential distribution with unknown parameter . Let 0

Problem 1. (Analysis of Variance) Let X1, X2, . .. Xn be random sample with finite mean /x and variance or, and Y1, Y2, . . . Ym be another random sample with finite mean My and variance o2. Assuming...

please help! will Like Let X1, ... , Xn be a random sample from gamma(a = 3, B = 1/11), and independently let Y1,..., Ym be a random sample form gamma(a = 4, B = 1/12). a) Using the statistics T =...

A random variable has the Pareto Distribution with parameters :30 > 0 and a > 0 if it has a continuous distribution with pdf, 0151:\" f(33|'130a0) : Slim-31 1 for m 2 330,01 > 0, and f(:c|:cg,a) = 0...

9.4 Let X1, ..., Xn be a random sample from a n(0, x ), and let Y1, . .., Ym be a random sample from a n(0, op ), independent of the Xs. Define A = ov /ox. (a) Find the level a LRT of Ho: A = do...

Let X1,..., Xn be a random sample from a n(0, 2X), and let Y1,..., Ym be a random sample from a n(0, 2Y), independent of the As. Define = 2Y/ 2X. a. Find the level a LRT of H0: = 0 versus H1: 0....

Statistics and Probability 5.(20pts) Let X1, ..., Xn be a random sample from N(u1, o?). Let Y1, ..., Yn be a random sample from N(#2, 02). Besides, X; is independent of Y; for all i, j. In addition,...

multiple choice questions 1-5, thanks Question 1 (1 point) Let 2 be a standard normal random variable. What is the probability that the absolute value of z is at least 1.66? O a) 0.1212 O b) 0.0970 O...

You are applying for auto loans where the local bank charges you an APR of 3.5% compounded monthly. Based on your income, the maximum amount you can pay is $550 per month for 4 years, where the...

A theoretical justification based on a certain material failure mechanism underlies the assumption that ductile strength of a material has a lognormal distribution. Suppose the values of the...

At lanuary 1 , 2 0 0 5 , Sheridan Company / s outstanding shares included the following 3 0 0 , 0 0 0 shares of 5 5 0 par value, 7 % cumulative prelerred stock Net ircome for 2 0 2 5 was $ 2 . 4 9 3...

What is your level of proficiency with Microsoft Office? What work have you done with Excel spreadsheets?

Reconsider the data in Exercise 6-76. Construct normal probability plots for two groups of the data: the first 40 and the last 40 observations. Construct both plots on the same axes. What tentative...

Construct a normal probability plot of the effluent discharge temperature data from Exercise 6-47. Based on the plot, what tentative conclusions can you draw?

Construct normal probability plots of the cold start ignition time data presented in Exercises 6-44 and 6-56. Construct a separate plot for each gasoline formulation, but arrange the plots on the...

A few years back, Dave and Jana bought a new home. They borrowed $230,415 at a fixed rate of 5.49% (15-year term) with monthly payments of $1,881.46. They just made their twenty-fifth payment and the...

Just Dew It Corporation reports the following balance sheet information for 2017 and 2018. 2018 JUST DEW IT CORPORATION 2017 and 2018 Balance Sheets Assets Liabilities and Owners' Equity 2017 2018...

11.4. Which of the following are relevant cash flows in the evaluation of a proposal to produce a new product? 11.5 Managers of central Embroidery have decided to purchase a new monogram machine and...