2.9.8 Let X~ Geometric(1/4), and let Y have probability function 1/6 y-2 y=5 0 otherwise Let...
The joint probability density function of random variables X and Y is given by f(x,y) ={10xy^2 0≤x≤y≤1,0 otherwise. (a) Compute the conditional probability fX|Y(x|y). (b) Compute E(Y) and P(Y >1/2). (c) Let W=X/Y. Compute the density function of W. (d) Are X and Y independent? Justify briefly.
5. Let X and Y be independent and identically distributed with marginal probability density function İf a> 0, otherwise, e-ea f(a)-( where >0 (a) [6 pts] Use the convolution formula to find the probability density function of X +Y (b) (6 pts) Find the joint probability density function of V= X + Y U=X+Y and
5. Let X and Y be independent and identically distributed with marginal probability density function İf a> 0, otherwise, e-ea f(a)-( where >0 (a) [6...
2. Let the joint probability density function of (X, Y) be given by {ay otherwise. 1 and 0 < y < 2, f(z,y) (a) [6 pts] Determine if X and Y are independent. (b) [6 pts] Find P{X+Y <1) B( (c) [6 pts) Find
2. Let the joint probability density function of (X, Y) be given by {ay otherwise. 1 and 0
4. Let X and Y have joint probability density function f(x,y) = 139264 oray3 if 0 < x, y < 4 and y> 4-1, otherwise. (a) Set up but do not compute an integral to find E(XY). (b) Let fx() be the marginal probability density function of X. Set up but do not compute an integral to find fx(x) when I <r54. (c) Set up but do not compute an integral to find P(Y > X).
5. Let X and Y have joint probability density function of the form Skxy if 0 < x +y < 1, x > 0 and y > 0, f(x,y)(, y) = { 0 otherwise. (a) What is the value of k? (b) Giving your reasons, state whether X and Y are dependent or independent. (c) Find the marginal probability density functions of X and Y. (d) Calculate E(X) and E(Y). (e) Calculate Cov(X,Y). (f) Find the conditional probability density function...
3. Let the random variables X and Y have the joint probability density function 0 y 1, 0 x < y fxy(x, y)y otherwise (a) Compute the joint expectation E(XY) (b) Compute the marginal expectations E(X) and E (Y) (c) Compute the covariance Cov(X, Y)
2. Let X and Y be continuous random variables with joint probability density function fx,y(x,y) 0, otherwise (a) Compute the value of k that will make f(x, y) a legitimate joint probability density function. Use f(x.y) with that value of k as the joint probability density function of X, Y in parts (b),(c).(d),(e (b) Find the probability density functions of X and Y. (c) Find the expected values of X, Y and XY (d) Compute the covariance Cov(X,Y) of X...
2.6.9 Let X have density function fx(x) = x/4 for 0 < x < 2, otherwise fx(x)=0. (a) Let Y = X. Compute the density function fy(y) for Y. (b) Let Z = X. Compute the density function fz(z) for Z.
The joint probability density function of random variables X and Y is given by f(x,y) ={10xy^2 0≤x≤y≤1,0 otherwise. (a) Compute the conditional probability fX|Y(x|y). (b) Compute E(Y) and P(Y >1/2). (c) Let W=X/Y. Compute the density function of W. (d) Are X and Y independent? Justify briefly.
Let f(x,y) = (1+xy)/4, if |x|<1 and |y|<1 and f(x,y) = 0, otherwise be the joint probability density function of (X, Y ). (a) Are X and Y independent? (b) Are X2 and Y 2 independent?