Example 16-21. X is a binomial variate with parameters n and p and Fo1, oz is an F-statistic with V1 and vz d.f. Prove that :P(X

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Answered: Example 16-21. X is a binomial variate…

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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Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(X)=-9 E (Z) = 1 E (Y)=-6 Var(Y)=28 Var(Z) = 47 Var (X)=44 Compute the values of the expressions below. E (2-Z) = 0 E(X+32)=0 -5 -2-Var(4X) = 0 E(-x²) = 0 Continue □ X S M 31 Ⓒ2022 McGraw Hill LLC. All Rights Reserved
Q5: Let X₁, X₂, ***9 X be a random sample with size n from n(0, 1). Show that the likelihood ratio for hypothesis: H₁:0=00 H₁:0#00 Leads to the inequality |x-02b. Is this a uniform most powerful test of the hypothesis?
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(d) A random sample consists of a single observation, r, from the Bin(6, 7) distribution, i.e. a binomial distribution with six trials. We are interested in testing: Ho = 0.50 vs. H₁: π = 0.75. A test rejects Ho if x = 6. i. Calculate the size of the test. ii. Calculate the power of the test.
Q.3. If the sample space is C = {x : 0 < x < ∞} and C CC where %3D C = {x : 8
hoosing among several different estimators of 0, select one that is unbiased. Example 9.3: Let X₁, X2, ..., Xn be a random sample from a population mean and variance o². Show that the sample variance, - Σ(x₁ - x)² = n-1 is an unbiased estimator of o². 5²
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: 14:41. Marks obtained by a number of students are assumed to be normally distributed with n 50 and variance 36. If 4 students are taken at random, what is the probability that exactly two of them will have marks over 62 ? 0(z) dz = 0-4772 where Z is N (0, 1).
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Prove two formulas for sample variance are equivalent. i.e. Σ(x - 7) _Σ – (Στ) η η-1 n-1
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Example 16-21. X is a binomial variate with parameters n and p and Fo1, 02 statistic with vị and v2 d.f. Prove that : is an F- P(X