Consider Z = 3.4X+3.9Y where X and Y are independent normal random variables. The mean and variance of X are 3.3 and 6.6, respectively. The mean and variance of Y are 2.6 and 4.5, respectively. (a) What is the covariance between Z and X? Your answer correct up to four decimal places. (b) What is the correlation between Z and X? Your answer correct up to four decimal places. (c) What is the E[Z|X=4.1]? Your answer correct up to four decimal places.

Consider Z = 3.4X+3.9Y where X and Y are independent normal random variables. The mean and variance of X are 3.3 and 6.6, respectively. The mean and variance of Y are 2.6 and 4.5, respectively. (a) What is the covariance between Z and X? Your answer correct up to four decimal places. (b) What is the correlation between Z and X? Your answer correct up to four decimal places. (c) What is the E[Z|X=4.1]? Your answer correct up to four decimal places.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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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