Let O, X1, X2,... be RVs. Suppose that, condi-tional on O = 0, X1, X2,... are independent and X is normally distributed2.3 Normal distributionwith mean e and variance o. Suppose that the marginal PDF of O is027(0) =e ER.e5.Calculate the mean and variance of O conditional on X1 = r1,...,Xn = In.

Answered: Image /qna-images/answer/2d4bda4d-8ad3-4353-b458-d16869837eed.jpg

Answered: Let 0, X1, X2,... be RVs. Suppose that,…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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9. (8') Let X,, X,, X, be a sample of size n=3 from a distribution with unknown mean u, -0 < u<0, where the variance o is a known positive number. Show that both à =i and ê, = 2X, + X, +5X, are unbiased estimators for H.
QUESTION 2 i) If U, and U, each have a normal distribution with mean 0 and variance 20². Furthermore, mu, (t) = etio for i = 1,2. Show that U and U2 are independent.
A population has a mean µ = 161 and a standard deviation o = 20. Find the mean and standard deviation of the sampling distribution of sample means with sample size n = 56. The mean is = μx (Round to three decimal places as needed.) and the standard deviation is o- = X 3 X
The first thing we need to do is check to see if the distribution is approximately normal. 50(0.6) = 30 and ng = 50(0.4) = 20 np = пр Since np 10 and nq ≥ 10, we can conclude that is approximately a normal distribution with • mean Up • standard deviation op = = 0.6 and pq n = = 0.6(0.4) 50 = pq n 0.24 50 (which is very close to what we saw in our simulation, standard error =0.063). standard error found in the simulation (standard error = 0.030)? ор nearest thousandth). Now find the approximation for samples of size 250. Is the standard deviation close to the = 0.0693 (Round to the Is the standard deviation close to the standard deviation (standard error) found in the simulation?
Explain at least two differences between the following two point estimations of the population variance. 22 = Σ'1(X, – X)2 n-1 62 _ Σ 1 (X - X)2 =1 = n
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