Let X1, X2,.......Xn be a random sample of size n from a continuous distribution symmetric about...

Question

Question

Let X_1, X_2,.......X_n be a random sample of size n from a continuous distribution symmetric about $\small \theta$ .

For testing H_0:= 10 vs H_1: $\small \theta$ < 10, consider the statistic T^- = $\tiny \sum_{i-1}^{n}$ Ri⁺(1- $\small \psi$ _i),

where $\small \psi$ _i =1 if X_i>10 , 0 otherwise; and R_i⁺ is the rank of (X_i - 10) among |X₁ -10|, |X₂-10|......|X_n -10|.

1. Find the null mean and variance of T^- .

2. Find the exact null distribution of T^- for n=5.

math Statistics-And-Probability

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

nlhor I-I ㄥ n (nt) nint) (2) 2 4 cs Scanned w CamScanner hope you like it.

Add a comment

Answer 2

Similar Homework Help Questions

Let X1, X2, ..., Xn be a random sample of size n from the distribution with...

Let X1, X2, ..., Xn be a random sample of size n from the distribution with probability density function To answer this question, enter you answer as a formula. In addition to the usual guidelines, two more instructions for this problem only : write as single variable p and as m. and these can be used as inputs of functions as usual variables e.g log(p), m^2, exp(m) etc. Remember p represents the product of s only, but will not work...
Let X1, . . . , Xn be a random sample from a triangular probability distribution...

Let X1, . . . , Xn be a random sample from a triangular probability distribution whose density function and moments are: fX(x) = * I{0 x b} a. Find the mean µ of this probability distribution. b. Find the Method Of Moments estimator µ(hat) of µ. c. Is µ(hat) unbiased? d. Find the Median of this probability distribution. I will thumbs up any portion or details of how to do this problem, thanks! We were unable to transcribe this...
Independent random samples X1, X2, . . . , Xn are from exponential distribution with pdfs...

Independent random samples X1, X2, . . . , Xn are from exponential distribution with pdfs , xi > 0, where λ is fixed but unknown. Let . Here we have a relative large sample size n = 100. (ii) Notice that the population mean here is µ = E(X1) = 1/λ , population variance σ^2 = Var(X1) = 1/λ^2 is unknown. Assume the sample standard deviation s = 10, sample average = 5, construct a 95% large-sample approximate confidence...

Let X1, X2, . . . , Xn be a random sample of size n from...

Let X1, X2, . . . , Xn be a random sample of size n from a normal population with mean µX and variance σ ^2 . Let Y1, Y2, . . . , Ym be a random sample of size m from a normal population with mean µY and variance σ ^2 . Also, assume that these two random samples are independent. It is desired to test the following hypotheses H0 : σX = σY versus H1 : σX...
1. Let X1, X2,... .Xn be a random sample of size n from a Bernoulli distribution...

1. Let X1, X2,... .Xn be a random sample of size n from a Bernoulli distribution for which p is the probability of success. We know the maximum likelihood estimator for p is p = 1 Σ_i Xi. ·Show that p is an unbiased estimator of p.
Let X1, X2, ..., Xn be a random sample from X which has pdf depending on...

Let X1, X2, ..., Xn be a random sample from X which has pdf depending on a parameter and (i) (ii) where < x < . In both these two cases a) write down the log-likelihood function and find a 1-dimensional sufficient statistic for b) find the score function and the maximum likelihood estimator of c) find the observed information and evaluate the Fisher information at = 1. f(20) We were unable to transcribe this image((z(0 – 2) - )dxəz(47)...

Let X1,X2,...,Xn denote independent and identically distributed random variables with variance 2. Which of the following...

Let X1,X2,...,Xn denote independent and identically distributed random variables with variance 2. Which of the following is sucient to conclude that the estimator T = f(X1,...,Xn) of a parameter ✓ is consistent (fully justify your answer): (a) Var(T)= (b) E(T)= and Var(T)= . (c) E(T)=. (d) E(T)= and Var(T)= We were unable to transcribe this imageWe were unable to transcribe this imageoe We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this...
Let X1,...,X10 be a random sample from N(θ1,1) distribution and let Y1,...,Y10 be an independent random sample from N(θ2,1) distribution. Let φ(X,Y ) = 1 if X < Y , −5 if X ≥ Y , and V= φ(Xi,Yj)...

Let X1,...,X10 be a random sample from N(θ1,1) distribution and let Y1,...,Y10 be an independent random sample from N(θ2,1) distribution. Let φ(X,Y ) = 1 if X < Y , −5 if X ≥ Y , and V= φ(Xi,Yj) . 1. Find v so that P[V>=v]=0.45 when 1=2. 2. Find the mean and variance of V when 1=2. 10 10 2 We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe...
Let X1, X2, ... , Xn be a random sample of size n from the exponential...

Let X1, X2, ... , Xn be a random sample of size n from the exponential distribution whose pdf is f(x; θ) = (1/θ)e^(−x/θ) , 0 < x < ∞, 0 <θ< ∞. Find the MVUE for θ. Let X1, X2, ... , Xn be a random sample of size n from the exponential distribution whose pdf is f(x; θ) = θe^(−θx) , 0 < x < ∞, 0 <θ< ∞. Find the MVUE for θ.

Let X1, X2, ...,Xn be a random sample of size n from a Poisson distribution with...

Let X1, X2, ...,Xn be a random sample of size n from a Poisson distribution with mean 2. Consider a1 = *1782 and în = X. Find RE(21, 22) for n = 25 and interpret the meaning of the RE in the context of this question.

Let X1, X2,.......Xn be a random sample of size n from a continuous distribution symmetric about...

Homework Answers

Add Answer to:
Let X1, X2,.......Xn be a random sample of size n from a continuous distribution symmetric about...

Post as a guest

Earn Coins

Let X1, X2, ..., Xn be a random sample of size n from the distribution with...

Let X1, . . . , Xn be a random sample from a triangular probability distribution...

Independent random samples X1, X2, . . . , Xn are from exponential distribution with pdfs...