Unformatted text preview: 1 and 0 < y < 1, g ( x,y ) = 0 elsewhere. (b) Find the joint density of ( ZX,ZY ). (c) Find the density of X X + Y . 4. Let X and Y be independent and identically distributed random variables each with a continuous density f ( t ) which is zero if t 6∈ [0 , 1], and not zero if t ∈ (0 , 1). (a) Find an integer n such that lim ε → 1 ε n P ± | ( X,Y )-± 1 2 , 1 2 ² | ² = δ, where δ ∈ (0 , ∞ ) and | ( a,b )-( c,d ) | is the Euclidean distance between these points. Evaluate δ in terms of f . (b) Find an integer n such that lim ε → 1 ε n P ( | X-Y | < ε ) = δ, where δ ∈ (0 , ∞ ). For which f is this δ minimized?...
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- Spring '09
- Variance, Probability theory, lim, probability density function, joint density