hw14 - For 0, determine P [ Y = X + ]. Problem 14B Compute...

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ENEE 324 ASSIGNMENT 14 Due Tue 10/27 Problem 14A X and Y are random nonnegative integers such that P [ X = i, Y = j ] = ( c · 2 - i - j , 0 i j ; 0 , otherwise. (i) (4 pts.) Determine, in terms of c , P [ X = i ] and P [ Y = j ] for every i 0 and j 0. (ii) (4 pts.) What is the value of c ? Are X and Y independent? Explain. (iii) (4 pts.) For j 0, determine P [ Y j ]. In each of the following parts, also sketch the event in question on the ( i,j ) grid. (iv) (4 pts.) For 0, determine P [ X + Y = 2 ]. (v) (4 pts.)
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Unformatted text preview: For 0, determine P [ Y = X + ]. Problem 14B Compute the following integrals: (6 pts.) RR R x (1 + y )-1 dxdy , where R = { ( x,y ) : 0 x 1 , x y 1 } . (7 pts.) RR R e-x dxdy , where R = { ( x,y ) : 0 y 2 x-1 } (7 pts.) RR R x 2 y dxdy , where R = { ( x,y ) : x , y , x 2 + y 2 4 }...
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