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 (  XY  < ε ) = δ, where δ ∈ (0 , ∞ ). For which f is this δ minimized?...
View
Full Document
 Spring '09
 Variance, Probability theory, lim, probability density function, joint density

Click to edit the document details