Let X and Y have joint pdf f(x,y)=k(x+y), for 0<=x<=1 and 0<=y<=1. a) Find k. b)...

Let X and Y have joint pdf f(x,y)=k(x+y), for 0<=x<=1 and 0<=y<=1.

a) Find k.

b) Find the joint cumulative density function of (X,Y)

c) Find the marginal pdf of X and Y.

d) Find Pr[Y<X²] and Pr[X+Y>0.5]

Expert Solution

orchestra answered 1 year ago

Let X and Y have the joint pdf f(x, y) = 8xy, 0 ≤ x ≤...

Let X and Y have the joint pdf f(x, y) = 8xy, 0 ≤ x ≤ y ≤ 1. (i) Find the conditional means of X given Y, and Y given X. (ii) Find the conditional variance of X given Y. (iii) Find the correlation coefficient between X and Y.

(a) Let X and Y have the joint pdf ???(?, ?)=1, 0≤x≤3/2, 0≤y≤1, zero elsewhere. Find:...

(a) Let X and Y have the joint pdf ???(?, ?)=1, 0≤x≤3/2, 0≤y≤1, zero elsewhere. Find: 1 The pdf of Z=X+Y 2 The pdf of Z=X.Y

Let X and Y have the following joint density function f(x,y)=k(1-y) , 0≤x≤y≤1. Find the value...

Let X and Y have the following joint density function f(x,y)=k(1-y) , 0≤x≤y≤1. Find the value of k that makes this a probability density function. Compute the probability that P(X≤3/4, Y≥1/2). Find E(X). Find E(X|Y=y).

let the continuous random variables X and Y have the joint pdf: f(x,y)=6x , 0<x<y<1 i)...

let the continuous random variables X and Y have the joint pdf: f(x,y)=6x , 0<x<y<1 i) find the marginal pdf of X and Y respectively, ii) the conditional pdf of Y given x, that is fY|X(y|x), iii) E(Y|x) and Corr(X,Y).

Let X and Y have joint PDF f(x) = c(e^-(x/λ + y/μ)) 0 < x <...

Let X and Y have joint PDF f(x) = c(e^-(x/λ + y/μ)) 0 < x < infinity and 0 < y < infinity with parameters λ > 0 and μ > 0 a) Find c such that this is a PDF. b) Show that X and Y are Independent c) What is P(1 < X < 2, 0 < Y < 5) ? Leave in exponential form d) Find the marginal distribution of Y, f(y) e) Find E(Y)

The joint PDF of X and Y is given by f(x, y) = C, (0< x<y<1)....

The joint PDF of X and Y is given by f(x, y) = C, (0< x<y<1). a) Determine the value of C b) Determine the marginal distribution of X and compute E(X) and Var(X) c) Determine the marginal distribution of Y and compute E(Y) and Var(Y) d) Compute the correlation coefficient between X and Y

Question

Let X and Y have joint pdf f(x,y)=k(x+y), for 0<=x<=1 and 0<=y<=1. a) Find k. b)...

Solutions

Expert Solution

Related Solutions

Let X and Y have the joint pdf f(x, y) = 8xy, 0 ≤ x ≤...

(a) Let X and Y have the joint pdf ???(?, ?)=1, 0≤x≤3/2, 0≤y≤1, zero elsewhere. Find:...

Let X and Y have the following joint density function f(x,y)=k(1-y) , 0≤x≤y≤1. Find the value...

let the continuous random variables X and Y have the joint pdf: f(x,y)=6x , 0<x<y<1 i)...

Let X and Y have joint PDF f(x) = c(e^-(x/λ + y/μ)) 0 < x <...

The joint PDF of X and Y is given by f(x, y) = C, (0< x<y<1)....

Let X and Y be continuous random variables with joint pdf f(x, y) = kxy^2 0...

Let the joint p.d.f f(x,y) = 1 for 0 <= x <= 2, 0 <= y...

Let (A,B) have joint PDF f(a,b)=(ca^2b^2 when 0 < a,b,a+b < 1 and 0 otherwise for...

Given the joint probability density function f(x ,y )=k (xy+ 1) for 0<x <1--and--0<y<1 , find...