Let X and Y have the following joint distribution: X Y012 12/16 1/16 5/16 2 1/161/16...
1. Let X and Y have a discrete joint distribution with ( P(X = x, Y = y) = {1, 10, if (x, y) = (-1,1) if x = y = 0 elsewhere Show that X and Y are uncorrelated but not independent. [5 points] 2. Let X and Y have a discrete joint distribution with f(-1,0) = 0, f(-1,1) = 1/4, f(0,0) = 1/6, f(0, 1) = 0, $(1,0) = 1/12, f(1,1) = 1/2. Show that (a) the two...
3. Let X and Y have a discrete joint distribution with Table 1: Joint discrete distribution of X and Y Values of Y -1 0 1 Values of X -1 1 į 0 1 1 0 -600-100 Then, find the following: • the marginal distribution of X; [2 points) • the marginal distribution of Y; [2 points] the conditional distribution of X given Y = -1; [2 points] Are X and Y are independent? Discuss with proper justification. (3 points)...
Let X and Y have the following joint distribution: X/Y 0 1 2 0 5/50 8/50 1/50 2 10/50 1/50 5/50 4 10/50 10/50 0 Further, suppose σx = √(1664/625), σy = √(3111/2500) a) Find Cov(X,Y) b) Find p(X,Y) c) Find Cov(1-X, 10+Y) d) p(1-X, 10+Y), Hint: use c and find Var[1-X], Var[10+Y]
Let X and Y have the following joint distribution: X/Y -1 1 0 0.2 0.15 2 0.1 0.2 4 0.25 0.1 a) Find the probability distributions for X and Y b) Find E[X] and E[Y] c) Find the probability that X is larger than 1 d) Find E[XY]
QUESTION 12 Let the random variable X and Y have the joint p.d.f. f(x,y) =(zy for 0< <2, 0 < y <2, and z<y otherwise Find P(0KY <1) 16 QUESTION 13 R eter to question 12. Find P(o < x <3I Y-1).
Let X and Y have the following joint distribution X/Y 0 1 0 0.4 0.1 1 0.1 0.1 2 0.1 0.2 a) Find Cov(4+2X, 3-2Y) b) Let Z = 3X-2Y+2 Find E[Z] and σ 2Z c) Calculate the correlation coefficient between X and Y. What does this suggest about the relationship between X and Y? d) Show that for two nonzero constants a and b Cov(X+a, Y+b) = Cov(X,Y)
10. Let X and Y have a discrete joint distribution with if (x,y) = (-1,1) P(X = 2, Y = y) = { = ; if x=y=0 = 0, elsewhere Find (a) the conditional distribution of Y given X = -1. (b) show that X and Y are uncorrelated but not independent. (C) Find the marginal distributions of X and Y.
Let the two-dimensional random variable (X, Y) have the joint density fx.r(x, y) = 16 - x - y)I(0, 2)(x)/(2,4,(y). (a) Find &[Y| X = x]. (6) Find &[Y|X = x]. © Find var (Y|X=x]. (d) Show that &[Y] = { [E[Y|X]]. (e) Find &[XY|X=x]. Tinomial distribution (multinomial with k + 1 =3) of two random variables The trinomial distribution (mu X and Y is given by fx.x(x, y) = x!y!(n - x - y)!' for x, y=0, 1, ...,...
the answer is y-7/12=-1/11(x-7/12) but I dont know why 5) Let X and Y have joint probability density function Graph the support of the joint random variable (X, Y). Find the Least squares regression line and graph it with the support 5) Let X and Y have joint probability density function Graph the support of the joint random variable (X, Y). Find the Least squares regression line and graph it with the support
(a) Let x, have a chi-squared distribution with parameter y, and let x, be independent of x, and have a chi-squared distribution with parameter vz Show that x2 + x, has a chi-squared distribution with parameter v, + vz Let y = x2 + x2. Identify the correct expression for Fyn). "1/2 - 2x212/2-12-(x1 + x2)/2 dx1 OFyly) = ' -X1/2 dx1 + -x212 dxz e 109) = 6 {1*(***) ** (*)*" + x2)120mg +6 (277(3)) -<*****@*)*** .(-)70%as C (7-(1)...