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Statistics / Probability and Statistical Inference 9 / Chapter 4.5 / Problem 4.5-4

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

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Let X and Y have a bivariate normal distribution with X = 70, 2 X = 100, Y = 80, 2 Y =

Chapter 4, Problem 4.5-4

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QUESTION:

Let X and Y have a bivariate normal distribution with \(\mu_X = 70, \sigma^2_X = 100, \mu_Y = 80, \sigma^2_Y = 169\), and \(\rho = 5/13\). Find

(a) E(Y | X = 72).

(b) Var(Y | X = 72).

(c) \(P(Y \le 84, | X = 72)\).

Questions & Answers

QUESTION:

Let X and Y have a bivariate normal distribution with \(\mu_X = 70, \sigma^2_X = 100, \mu_Y = 80, \sigma^2_Y = 169\), and \(\rho = 5/13\). Find

(a) E(Y | X = 72).

(b) Var(Y | X = 72).

(c) \(P(Y \le 84, | X = 72)\).

ANSWER:

Step 1 of 4

Given that,

Let X and Y have a bivariate normal distribution with and

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