4. Suppose that X and X2 have joint PDF: jXiXy(Xi,T2)=Í : otherwise 0 (a) Use the...
Suppose that X1 and X2 have joint PDF xx2(,2)o 0 : otherwise (a) Use the transformation technique to find the joint PDF of Yǐ and Ý, where Yi = X1/X2 and Y2-X2 (b) Using your answer to part (a), find and identify the distribution of Yi
4. Suppose that X and X2 have joint PDF 0 otherwise (a) Use the transformation technique to find the joint PDF of y, and where x,/x, and Y, = X2 (b) Using your answer to part (a), find and identify the distribution of Y.
thanks Suppose that Xi and X2 are independent random variables each having PDF: : otherwise (a) Use the transformation technique to find the joint PDF of Yi and Ya where Y-X1 and ½ = Xi +X2. (b) Using your answer to part (a), and the fact that o Vu(1-u) find and identify the distribution of Y2.
5. Suppose that X and X2 are independent random variables each having PDF: each having PDF: : otherwise (a) Use the transformation technique to find the joint PDF of Yi and Yo where Y -X and ½ = Xi +Xg. (b) Using your answer to part (a), and the fact that find and identify the distribution of Y
12. (8 Pts.) Let Xi and X2 have the joint PDF Let Yi Xi/X2 and Y2 = Xy. Find the joint PDF of(H.)a). Are Y1 and Y2 independent?
Q3. Suppose that X, Y have joint pdf a for x2 + y2 0 otherwise. 1. fxy(x, y)- (a) Find the value of a so that fxy(x, y) is a valid pdf. b) Find the marginal pdf for X Hint: It is helpful to sketch the region of the ry-plane where the pdf is non-zero
Consider two random variables X and X2 with the joint pdf Nn.za) ={Orm ekewhere 1, o?r2 < 1 Let Y X,X2 and Y2X2 be a joint transformation of (Xi, X2) (a) Find the support of (Y.%) and sketch it. (b) Find the inverse transformation. (c) Compute the Jacobian of the inverse transformation (d) Compute the joint pdf of (Yi, Y2) (e) Derive the marginal pdf of Y? from the joint pdf of (y,,Y2).
Pa Suppose that (X1, X2) ~ N(0,0,1,1,0). It follows from this that the joint PDF of (X1, Xy) is given by fxıx(31,09) - exp(+34 +23) Furthermore, if GE Thte and 12(x3 + x2) - tao V5 (Xi-X) que Then (Y1,Y,) ~ N(0,0, 1, 1,0) as well. (a) If X, < X2, what are the possible values of Y1 and Y2? (b) If Y2 < 0, what are the possible values of X, and X,? (c) What is the marginal distribution...
Exercise 7 (team 5) Let Xi and X2 have joint pdf x1 + x2 if0<x1 < 1 and 0 < x2 < 1 /h.x2 (x1,x2) = 0 otherwise. When Y1 X1X2 derive the marginal pdf for Y.
Suppose that (X1, X2) N (0,0,1,1,0). It follows from this that the joint PDF of (X1, X2) is given by Ixvx:(21,2) = exp (1} (27 +23)) Furthermore, if 1 Y Tā (X1 + X2) and Y2 (X1 - X2) Then (Y1,Y) ~ N(0,0,1,1,0) as well. (a) If X1 <X2, what are the possible values of Y¡ and Y2? (b) If Y, <0, what are the possible values of Xi and X,? (c) What is the marginal distribution of Yg? (d)...