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(c) P (V, > cV2) = a. (d) P [Z? >c (Vị + V2)] = a. (e) P[ V,/ (V, + V½) > c] = a.

(c) P (V, > cV2) = a. (d) P [Z? >c (Vị + V2)] = a. (e) P[ V,/ (V, + V½) > c] = a.

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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7. Suppose Z~N(0,1), V~x²(1), V~x²(2) and all random variables are independent. Consider the following notation. x (a; m) is the upper a quantile of x (m) distribution, t(a; m) is the upper a quantile of t(m) distribution, F(a; m,, m2) is the upper a quantile of F(m,, 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 (V, + V2 > c) = a. (b) P (Z > c/V.) = a. (c) P (V, > cV2) = a. (d) P [Z? > c (V1 + V2)] = a. (e) P[ V/ (V, + V½) > c] = a. %3D
Transcribed Image Text:7. Suppose Z~N(0,1), V~x²(1), V~x²(2) and all random variables are independent. Consider the following notation. x (a; m) is the upper a quantile of x (m) distribution, t(a; m) is the upper a quantile of t(m) distribution, F(a; m,, m2) is the upper a quantile of F(m,, 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 (V, + V2 > c) = a. (b) P (Z > c/V.) = a. (c) P (V, > cV2) = a. (d) P [Z? > c (V1 + V2)] = a. (e) P[ V/ (V, + V½) > c] = a. %3D
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