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.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 3CR
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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.
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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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