X, P(-e <

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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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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Let (X, : n > 1) be an infinite sequence of random variables. Consider the following
statements:
Statement A: If X, is normally distributed with mean 0 and variance rn, then for all
e > 0,
P(-e <
e) → 1
as n → 0.
Statement B: If X, has a x? distribution withn degrees of freedom, then X,
converges to some X in distribution as n → ∞, with P(X = 0) = 1.
Statement C: If X, has a t-distribution with n degrees of freedom, then X,
converges to some X in distribution as n → 0, with X having a continuous
distribution and satisfies P(X<1) = 0.48.
Which of the statements are true?
VI
Transcribed Image Text:Let (X, : n > 1) be an infinite sequence of random variables. Consider the following statements: Statement A: If X, is normally distributed with mean 0 and variance rn, then for all e > 0, P(-e < e) → 1 as n → 0. Statement B: If X, has a x? distribution withn degrees of freedom, then X, converges to some X in distribution as n → ∞, with P(X = 0) = 1. Statement C: If X, has a t-distribution with n degrees of freedom, then X, converges to some X in distribution as n → 0, with X having a continuous distribution and satisfies P(X<1) = 0.48. Which of the statements are true? VI
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