Let X and Y have bivariate normal distributions with μX = 70, μY = 80, σ2X = 100,σ2Y = 169, and ρ = 5/13. Find P(Y ≤86|X = 76).

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Answered: Let X and Y have bivariate normal…

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter4: Writing Linear Equations

Section: Chapter Questions

Problem 12CR

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Let X and Y have bivariate normal distributions with μ_X = 70, μ_Y = 80, σ²_X = 100,
σ²_Y = 169, and ρ = 5/13. Find P(Y ≤86|X = 76).

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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