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L UULIOL A (a) Evaluate the conditional distribution K(y/x=1), given the joint probability function f(x,y)= e-*-,x>0,y>0. 4 (bl ynloin the 1 1 :
If X and Y have a joint density given by f(x, y) = 2, for 0 < y < x < 1 0, elsewhere (a) If V = −lnX, what is the density of V ? (b) If V = −lnX and W = X + Y , what is the joint density of V and W? Sketch the region for which the joint density is nonzero.
The joint density function for X and Y is given as: f(x, y) = kxy for 0 < x < 2y < 1. Find the value of the constant k for which the p.d.f is legitimate. If the video does not work, click here to go to YouTube directly.
Assume that the joint density function of X and Y is given by f (x, y) = 4,0 < x < 2,0 < y = 2 and f (x, y) = 0 elsewhere. (a) Find P (X < 1, Y > 1). (b) Find the joint cumulative distribution function F(x, y) of the two random variables. Include all the regions. (c) Find P (X<Y). (d) Explain how the value of P (1 < X < 2,1 < Y < 2)...
Let the joint density function of X and Y be given by the following x +y for 0 < x < 1 and 0 < y < 1 f(x, y) = 0 otherwise Find E[X], E[Y], Var[X], Var[Y], Cov(X,Y), and px,y Find E[X]Y], E[E[X|Y]], and Var[X|Y]. Find the moment generating function Mx,y(t1, t2)
The joint density of X and Y is given as f(x, y) = 4xy, 0 < x, 1 and 0 < y < 1. (a). Find the marginal distribution of Y, fY (y). (b). Find E[X|Y = 1/2]. (c). Find P(X < .3|Y < .2).
2) Conditional probability distribution of X given y 1 and yo17 C) 0.5 x/ 2) Conditional probability distribution of X given y 1 and yo17 C) 0.5 x/
Calculate the i.) conditional probability density function of Y given X=10, ii.) conditional mean and variance of Y given X = 10 3 6 0 10 20 0.05 0.41 0.08 0.1 0.11 0.25 3 6 0 10 20 0.05 0.41 0.08 0.1 0.11 0.25
Suppose Y is uniformly distributed on (0,1), and that the conditional distribution of X given that Y = y is uniform on (0, y). Find E[X]and Var(X).
Question 1. The joint distribution of X and Y is given. Are X and Y independent? fx.y(2, ) X/Y 1 2 3 0.06 0.42 0.12 2 0.04 0.28 0.08 Check all fx,y(2,y) = fx(x)fy(y), are they equal? What you can say about X and Y? Question 2. Consider the following joint PMF 2,y,z fx.y.z(2,y,) 100 1/4 1/4 010 1/4 1/4 001 1/4 1. Find the PMF of (X,Y). 2. Are (X,Y) independent?