The problem statement is as follows:"The random variable \( X \) is distributed normally with mean \( \mu_X \) and variance 6, and the random variable \( Y \) is normally distributed with mean 8 and variance \( \sigma_Y^2 \). \( 2X - 3Y \) is distributed normally with mean 12 and variance 42.Calculate the values of \( \mu_X \) and \( \sigma_Y \) respectively. Assume independence!"Options provided are:- a. \( \mu_X = -6 \) and \( \sigma_Y = 2 \)- b. \( \mu_X = 18 \) and \( \sigma_Y = \sqrt{2} \)- c. \( \mu_X = -6 \) and \( \sigma_Y = \sqrt{2} \)- d. \( \mu_X = 12 \) and \( \sigma_Y = \sqrt{42} \)

Answered: Image /qna-images/answer/2aa0cd87-018b-4dcc-9da4-fd4b3f0b4363.jpg

Answered: The random variable X is distributed…

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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A nail is needed to hang up a 50 lb painting on a wall. A technician has two nails in his pocket, where the probability that both nails meet the specific weight of the painting is 50%, the probability that only one of them meets the specific weight is 20%, and the probability that neither of them meets the specific weight is 30%. If the number of nails that meet the specification is a random variable, find the variance of the data of that random variable.
Which one is correct?
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