5.4.([1] 5.6) The joint density function for Y1 and Y2 is f(y1,92) = {o 0 <...
5.3.([1] 5.5) The joint density of Y and Y2 is given by 0 < y2 < y1 <1 else f(y1.92) = {3 a) Find F (33) = P[Y; <z, Y s. b) Find P[Y2 = ").
Let Yı, Y, have the joint density S 2, 0 < y2 <yi <1 f(y1, y2) = 0, elsewhere. Use the method of transformation to derive the joint density function for U1 = Y/Y2,U2 = Y2, and then derive the marginal density of U1.
2. Let the random variables Y1 and Y, have joint density Ayſy22 - y2) 0<yi <1, 0 < y2 < 2 f(y1, y2) = { otherwise Stom.vn) = { isiml2 –») 05451,05 ms one a independent, amits your respon a) Are Y1 and Y2 independent? Justify your response. b) Find P(Y1Y2 < 0.5). on the
3. Let (X1, X2) have the joint p.d.f 1 if 0 <1,0 < <1 f(1, ) else Find P(X1X2 < 0.5)
Suppose a joint probability density function for two variables X and Y is given as follows: {24x0, if 0 < x < 1,0 < y < 1 f(x, y) = otherwise Please find the probability p (w > 1) =? 3
the joint probability density function is given by 1. The joint probability density function (pdf) of X and Y is given by fxy(x,y) = A (1 – xey, 0<x<1,0 < y < 0 (a) Find the constant A. (b) Find the marginal pdfs of X and Y. (c) Find E(X) and E(Y). (d) Find E(XY).
X1 and X2 are IID with the density: a) joint density with r.v. Y1 = X1 and Y2 = X1 + X2 (I think this might be transformation but I'm stuck after) b) marginal density for Y2 f(x) = V2nz exp (-2) , for x>0,
Question-2 Consider the joint uniform density function C for 22 + y2 < 4, f(x,y) 0 otherwise. What is the value of c? 0 What is P(X<0)? What is P(X <0, Y <0)? What is f( x | y=1)?
If two random variables have the joint density (x + y2), for 0 < x < 1, 0 < y < 1 0, elsewhere. find the probability that 0.2 < X < 0.5 and 0.4 <Y < 1.6. With reference to the previous Problem 6, find both marginal densities and use them to find the probabilities that a. X > 0.8; b. Y < 1.5.
Is a joint density function? If yes, assume it is the joint density function of r.v.s X and Y , and compute the marginal densities of X and Y . f(r,y) = { " 0 <y<<11 , otherwise