Let X₁,..., Xn be a random sample from a n(0,0²) population, o² known. An LRTof Ho: 0 = 0o versus H₁: 000 is a test that rejects Ho if X - 0o\/(o/√√n) > c.(a) Find an expression, in terms of standard normal probabilities, for the power func-tion of this test.(b) The experimenter desires a Type I Error probability of .05 and a maximum TypeII Error probability of .25 at 0 = 0o + o. Find values of n and c that will achievethis.

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

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Textbook: Statistical Inference Casella and Berger
Let X and Y be independent random variables such that Var[X] = 4.8 and Var[Y ] = 9.7. [a] How can we prove that 2X and 3Y are independent? [b] What is the standard deviation of 2X + 3Y?
Let X = ((X1,Y1),...,(X, Yn)) be a sample from a bivariate normal population. Show that the distributions of X form a five-parameter exponential family and identify п, В, Г, and h.
Let X1 ,X be a random sample from N(u, o?). The sample variance S2 is defined by (X- %3D n-1 im1 (n-1)S2 (a) Using the fact that two constants a and b satisfying: has a xn-1) distribution, explain how we can get (n-1)S2 S6 =1-a, (1) where a xo/2(n-1) and b xa/2(n-1) are critical values that can be obtained from a x-table. %3D
Suppose that a random man's weight from a certain population is M~ Normal (μ = 200, o²49) and a random woman's weight is W ~ Normal( 140, o² = 25). If M and W are independent, what is the variance of the difference between a man's weight and a woman's weight, i.e. Var (M-W)? (a) 340 (b) 24 (c) 140 (d) 200 (e) None of the above
A random sample of size n1 = 15 is selected from a normal population with a mean of 75 and a standard deviation of 9. A second random sample of size n2 = 9 is taken from another normal population with mean 69 and standard deviation 15. Let X1 and X2 be the %3D two sample means. Find: (a) The probability that X - X2 exceeds 3. (b) The probability that 4.9 < X – X2 < 5.9. Round your answers to two decimal places (e.g. 98.76). (a) i (b)
Suppose that X₁,..., Xn are i.i.d. from a normal population with mean μ and variance o². Calculate the expected value and the variance of the sample mean X and find the distribution of √n(X − µ).
If X is a negative binomial rv, then Y= r+Xis the total number of trials necessary to obtainr S’s. Obtain the mgf of Y and then its mean valueand variance. Are the mean and variance intuitively consistent with the expressions for E(X)and V(X)? Explain
Let X-1: correct, X=0 : wrong And P= Pr(X=1)=2/5 What is the variance? .32 O.6 O .4
Suppose that a medical test has a 85% chance of detecting a disease if the person has it (P(PT|D)=0.85) and a 90% chance of correctly indicating that the disease is absent if the person really does not have the disease (P(NT|Dc=0.90). Suppose that 95% of the population does not have the disease P(Dc)=0.95 What is the probability that a randomly chosen person will test negative P(NT)?

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