f(x,y)=275(2x2y+xy2)for0≤x≤3and1≤y≤2 a)Calculate marginal probability density: fX(x). b)Calculate marginal probability density: fY(y). c)Compute E[X], E[Y], and E[X+Y]. d)Compute E[X2], E[Y2], E[XY], and E[(X + Y)2]e)Compute Var (X+Y), Var(X), and Var(Y) and check that:Var (X+Y) ≠ Var(X) + Var(Y).
f(x,y)=275(2x2y+xy2)for0≤x≤3and1≤y≤2 a)Calculate marginal probability density: fX(x). b)Calculate marginal probability density: fY(y). c)Compute E[X], E[Y], and E[X+Y]. d)Compute E[X2], E[Y2], E[XY], and E[(X + Y)2]e)Compute Var (X+Y), Var(X), and Var(Y) and check that:Var (X+Y) ≠ Var(X) + Var(Y).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the variables X and Y with the following joint probability density:f(x,y)=275(2x2y+xy2)for0≤x≤3and1≤y≤2
a)Calculate marginal probability density: fX(x).
b)Calculate marginal probability density: fY(y).
c)Compute E[X], E[Y], and E[X+Y].
d)Compute E[X2], E[Y2], E[XY], and E[(X + Y)2]e)Compute Var (X+Y), Var(X), and Var(Y) and check that:Var (X+Y) ≠ Var(X) + Var(Y).
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