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Suppose X follows an exponential distribution with parameter A, then P(X ≤ 1|X ≤ 2) = e-^. (b) For a random variable X, suppose P(X>0) > P(X <0). True or False: The expectation of X must be positive. (c) Let ₁ and ₂ be two estimators of a parameter 0, where ê, has a strictly higher variance than 2. True or False: If the MSE criterion chooses the estimator ₁, then 2 must be biased.

Suppose X follows an exponential distribution with parameter A, then P(X ≤ 1|X ≤ 2) = e-^. (b) For a random variable X, suppose P(X>0) > P(X <0). True or False: The expectation of X must be positive. (c) Let ₁ and ₂ be two estimators of a parameter 0, where ê, has a strictly higher variance than 2. True or False: If the MSE criterion chooses the estimator ₁, then 2 must be biased.

MATLAB: An Introduction with Applications
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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Answer all of the following true-false questions. To obtain credit, you must write your answer (either TRUE or FALSE) in the box, and then briefly justify your answer with few sentences or computations. No points will be awarded for answers without justification. If possible, use math to back up your conclusion. For FALSE statements, you may want to provide a counterexample or explain how to change the statement to make it true. Note: An answer of TRUE means always true under the given assumptions. (a) Suppose X follows an exponential distribution with parameter λ, then P(X ≤ 1|X ≤ 2) = e-^. (b) For a random variable X, suppose P(X>0) > P(X < 0). True or False: The expectation of X must be positive. (c) Let ₁ and 2 be two estimators of a parameter 0, where Ô, has a strictly higher variance than 2. True or False: If the MSE criterion chooses the estimator ₁, then 2 must be biased.
Transcribed Image Text:Answer all of the following true-false questions. To obtain credit, you must write your answer (either TRUE or FALSE) in the box, and then briefly justify your answer with few sentences or computations. No points will be awarded for answers without justification. If possible, use math to back up your conclusion. For FALSE statements, you may want to provide a counterexample or explain how to change the statement to make it true. Note: An answer of TRUE means always true under the given assumptions. (a) Suppose X follows an exponential distribution with parameter λ, then P(X ≤ 1|X ≤ 2) = e-^. (b) For a random variable X, suppose P(X>0) > P(X < 0). True or False: The expectation of X must be positive. (c) Let ₁ and 2 be two estimators of a parameter 0, where Ô, has a strictly higher variance than 2. True or False: If the MSE criterion chooses the estimator ₁, then 2 must be biased.
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