Let X and Y have the joint PDF f(x) = { 1/2 0 < x +...

Let X and Y have the joint PDF

f(x) = { 1/2 0 < x + y < 2, x > 0, y > 0 ;

{ 0 elsewhere

a) sketch the support of X and Y

b) Are X and Y independent? Explain.

c) Find P(x<1 and y<1.5)

Expert Solution

Probability content calculation from the joint density function

milcah answered 2 months 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.

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]

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

Let X and Y be continuous random variables with joint pdf f(x, y) = kxy^2 0 < x, 0 < y, x + y < 2 and 0 otherwise 1) Find P[X ≥ 1|Y ≤ 1.5] 2) Find P[X ≥ 0.5|Y ≤ 1]

(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 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)

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

Let the joint p.d.f f(x,y) = 1 for 0 <= x <= 2, 0 <= y <= 1, 2*y <= x. (And 0 otherwise) Let the random variable W = X + Y. Without knowing the p.d.f of W, what interval of w values holds at least 60% of the probability?

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

Let X and Y have the joint pdf f(x,y)=(3/2)x^2 (1-|y|) , -1<x<1, -1<y<1. Calculate Var(X). Calculate...

Let X and Y have the joint pdf f(x,y)=(3/2)x^2 (1-|y|) , -1<x<1, -1<y<1. Calculate Var(X). Calculate Var(Y). P(−X≤Y).

Let X and Y have the joint probabilitydensity function (pdf):?(?, ?) = 3/2 ?2(1...

Let X and Y have the joint probability density function (pdf): f(x, y) = 3/2 x2(1 − y), − 1 < x < 1, − 1 < y < 1 Find P(0 < Y < X). Find the respective marginal pdfs of X and Y. Are X and Y independent? Find the conditional pdf of X give Y = y, and E(X|Y = 0.5).

Question