Let X and Y have a bivariate normal distribution. Find two
Chapter 4, Problem 9E(choose chapter or problem)
Let \(X\) and \(Y\) have a bivariate normal distribution. Find two different lines, \(a(x)\) and \(b(x)\), parallel to and equidistant from \(E(Y \mid x)\), such that
\(P[a(x)<Y<b(x) \mid X=x]=0.9544\)
for all real \(x\). Plot \(a(x), b(x)\), and \(E(Y \mid x)\) when \(\mu_{X}=2\), \(\mu_{Y}=-1, \sigma_{X}=3, \sigma_{Y}=5\), and \(\rho=3 / 5\).
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