7. Suppose Z~N(0,1), V₁~x²(1), V₂~x² (2) and all random variables are independent. Consider the following notation. x² (a; m) is the upper a quantile of x² (m) distribution, t(a; m) is the upper a quantile of t(m) distribution, F(a; m₁, m₂) is the upper a quantile of F(m₁, m₂) distribution. For example: P (V₂>c)= a ⇒c= x²(a; 2). In each of the following, write the constant c in terms of the appropriate quantile. (a) P (V₁ + V₂> c) = a. (b) P(Z > c√V₁) = a. (c) P (V₁ > cV₂) = (d) P [Z² > c (V₁ + V₂)] = a. (e) P[V₁/ (V₁ + V₂) >c] = a. = α.
7. Suppose Z~N(0,1), V₁~x²(1), V₂~x² (2) and all random variables are independent. Consider the following notation. x² (a; m) is the upper a quantile of x² (m) distribution, t(a; m) is the upper a quantile of t(m) distribution, F(a; m₁, m₂) is the upper a quantile of F(m₁, m₂) distribution. For example: P (V₂>c)= a ⇒c= x²(a; 2). In each of the following, write the constant c in terms of the appropriate quantile. (a) P (V₁ + V₂> c) = a. (b) P(Z > c√V₁) = a. (c) P (V₁ > cV₂) = (d) P [Z² > c (V₁ + V₂)] = a. (e) P[V₁/ (V₁ + V₂) >c] = a. = α.
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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