Let X, ... , X, be a random sample from N(0,1) , 0 E R , find UMVUEof e-0?Let X,, ... , X, be a random sample from N(o, 0²) , 0 > 0, find UMVUEof 02?•.

denotes a random sample from the normal distribution .The UMVUE of must be calculated.

Answered: Let X₁, . . ., Xn be a random sample…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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a) Let X₁, X₂, X3,..., X, be a random sample of size n from population X. Suppose that X~N(0, 1) you and Y = -√n. VR i) Show that the standard score of the sample mean X, is equal to Y. ii) Show that the mean and variance of the random variable Y are 0 and 1, respectively. iii) Show using the moment generating function technique that Y is a standard normal rando... variable. iv) What is the probability that Y² is between 0.02 and 5.02? b) Let X₁, X₂, X, and Y₁, Y₂.... Y be random samples from populations with moment generating functions Mx, (t) = eat+t² and My (t) = (-), respectively. 25 i) Find the sampling distribution of the statistic W = X₁ + 2X₂ X3 + X₁ + X5. ii) What is the value of the sample size n, if PIX(X-X)2> 68.3392] = 0.025? iii) What is the value of the sample size m, if P(|Y-Hy ≥10) <0.04? QUESTION A
Q Let Z be a standard normal random variable 2. Show that E[Z^*'] = n E [z"-¹]. to compute E [24] Use the result
Suppose that discrete random variable X~uni[1,2,3] A random sample of n=36 is selected from this population. Find the probability that the sample mean is greater than 2.1 but less than 2.5, assuming that the sample mean would be measured to the nearest tenth.
If X is uniform random variable on interval (2,7) then the expexted value of X equal 9/2 (1/2 5/2
Let X1, X2,...X, be a random sample from f(x,e) = -.0 < x< 8, then T= max(X,} is a %3D complete statistic for the parameter 0 Select one: O True False
50. Let X₁, X2, ..., X50 be i.i.d. with E(X) = 25 and V(X₂) = 10. Consider the random variable defined by 50 X₁ the sample average X = Σ Apply the Central Limit Theorem to answer the following: n i=1 (a) What is the approximate distribution of X (include parameter(s))? (b) Approximate P(X> 25.5). (c) Approximate P(|X-25 <0.8). (d) Approximate the 0.975 quantile (97.5th%tile) of X.
URGENT
Prove the following
5. Let (*1, x2, .., rn) be n independent random sample of size n from a uniform distribution on the interval [01,02]; (a) find the c.d.f of, X(1), the minimum order statistic (b) find the c.d.f of, X(n), the maximum order statistic (c) Hence, find the mean and variance of X(1) and X(n)-
a) Let X₁, X2, X3,..., X₁ be a random sample of size n from population X. Suppose that X follows an exponential distribution with parameter 0 and Y = ===1 X₁. n b) i) Show that y follows a chi-square distribution with 2n degrees of freedom. ii) What is the value of the sample size n, if P(Y > 20.4831) = 0.025? iii) What is the value of sample size n, if P(|Y - 2n| <40) ≥ 0.025? iv) Use the Central Limit Theorem to compute P(100 < Y < 115), for n = 40. Let X₁, X2, ..., X5 be a random sample of size 5 from the standard normally population. If the statistic Y is given by Y = X1 X2 X3 ₁²+X3² +X5² i) Briefly explain why Y follows a Student's t distribution with 3 degrees of freedom. ii) Compute the probability that Y is between 2.35 and 5.84. iii) What is the mean and variance of the statistic Y?
9. Let X₁, X2, ..., X5 be a random sample from a distribution with mean and variance 5 X₁, find Cov(X₁, X) 2. If X= = i=1

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Let X₁, . . ., Xn be a random sample from N(0, 1), 0 = R, find UMVUE of e-? Let X₁, ..., Xn be a random sample from N(O, 02), 0 > 0, find UMVUE of 02?