Question

Let X1, X2, · · · , Xn (n ≥ 30) be i.i.d observations from N(µ1,...

Let X1, X2, · · · , Xn (n ≥ 30) be i.i.d observations from N(µ1, σ12 ) and Y1, Y2, · · · , Yn be i.i.d observations from N(µ2, σ22 ). Also assume that X's and Y's are independent. Suppose that µ1, µ2, σ12 , σ22  are unknown. Find an approximate 95% confidence interval for (µ1µ2).

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Given,

X's and Y's are independent.

Here, we consider the null hypothesis

Then the test statistic is given as--

where

and

For a 95% confidence interval & the interval for is given by--

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let (X1, Y1), . . . ,(Xn, Yn), be a random sample from a bivariate normal...
Let (X1, Y1), . . . ,(Xn, Yn), be a random sample from a bivariate normal distribution with parameters µ1, µ2, σ2 1 , σ2 2 , ρ. (Note: (X1, Y1), . . . ,(Xn, Yn) are independent). What is the joint distribution of (X ¯ , Y¯ )?
5. Let a random sample, X1, X2, ..., Xn of size n = 10 from a...
5. Let a random sample, X1, X2, ..., Xn of size n = 10 from a distribution that is N(μ1, σ2 ) give ̄x = 4.8 and s 2+ 1 = 8.64 and a random sample, Y1, Y2, ..., Yn of size n = 10 from a distribution that is N(μ2, σ2 ) give y ̄ = 5.6 and s 2 2 = 7.88. Find a 95% confidence interval for μ1 − μ2.
Suppose that X1, X2, . . . , Xn are independent identically distributed random variables with...
Suppose that X1, X2, . . . , Xn are independent identically distributed random variables with variance σ2. Let Y1 = X2 +X3 , Y2 = X1 +X3 and Y3 = X1 + X2. Find the following : (in terms of σ2) (a) Var(Y1) (b) cov(Y1 , Y2 ) (c) cov(X1 , Y1 ) (d) Var[(Y1 + Y2 + Y3)/2]
Let X1,X2,...,Xn be i.i.d. (independent and identically distributed) from the uniform distribution U(μ,μ+1) where μ∈R is...
Let X1,X2,...,Xn be i.i.d. (independent and identically distributed) from the uniform distribution U(μ,μ+1) where μ∈R is unknown. Find a minimal sufficient statistic for μ parameter.
Suppose that X1, X2,   , Xn and Y1, Y2,   , Yn are independent random samples from populations with...
Suppose that X1, X2,   , Xn and Y1, Y2,   , Yn are independent random samples from populations with means μ1 and μ2 and variances σ12 and σ22, respectively. It can be shown that the random variable Un = (X − Y) − (μ1 − μ2) σ12 + σ22 n satisfies the conditions of the central limit theorem and thus that the distribution function of Un converges to a standard normal distribution function as n → ∞. An experiment is designed to test...
Let X1, X2, ..., Xn be a random sample (of size n) from U(0,θ). Let Yn...
Let X1, X2, ..., Xn be a random sample (of size n) from U(0,θ). Let Yn be the maximum of X1, X2, ..., Xn. (a) Give the pdf of Yn. (b) Find the mean of Yn. (c) One estimator of θ that has been proposed is Yn. You may note from your answer to part (b) that Yn is a biased estimator of θ. However, cYn is unbiased for some constant c. Determine c. (d) Find the variance of cYn,...
Let X1,X2...Xn be i.i.d. with N(theta, 1) a) find the CR Rao lower-band for the variance...
Let X1,X2...Xn be i.i.d. with N(theta, 1) a) find the CR Rao lower-band for the variance of an unbiased  estimator of theta b)------------------------------------of theta^2 c)-----------------------------------of P(X>0)
Let n ≥ 2 and x1, x2, ..., xn > 0 be such that x1 +...
Let n ≥ 2 and x1, x2, ..., xn > 0 be such that x1 + x2 + · · · + xn = 1. Prove that √ x1 + √ x2 + · · · + √ xn /√ n − 1 ≤ x1/ √ 1 − x1 + x2/ √ 1 − x2 + · · · + xn/ √ 1 − xn
1. Let x ∼ Np(µ, Σ). (1) Find the distribution of xp conditional on x1, ....
1. Let x ∼ Np(µ, Σ). (1) Find the distribution of xp conditional on x1, . . . , xp−1. (2) Suppose Σ =(1 ρ ρ 1 )and let y1 = x1 + x2 and y2 = −x1 + x2. Determine the joint distribution of y1 and y2. (3) Suppose Σ =( σ11 σ12 σ21 σ22 )and define y1 and y2 as in part (2).Determine the joint distribution of y1 and y2. Determine the conditional distribution y2 given y1.
let X1 X2 ...Xn-1 Xn be independent exponentially distributed variables with mean beta a). find sampling...
let X1 X2 ...Xn-1 Xn be independent exponentially distributed variables with mean beta a). find sampling distribution of the first order statistic b). Is this an exponential distribution if yes why c). If n=5 and beta=2 then find P(Y1<=3.6) d). find the probability distribution of Y1=max(X1, X2, ..., Xn)
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT