Question

Let (X, Y ) have joint cdf F, and let G be the cdf of the...

Let (X, Y ) have joint cdf F, and let G be the cdf of the random variable X + Y . Show that F(x, x) ≤ G(2x) for all x ∈ R

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Let A = (X x, Y x)

Hence, P(A) = P(X x, Y x) = F(x, x)

Let, B = (X + Y 2x)

Hence, P(B) = P(X + Y 2x) = G(2x)

Note that, X x and Y x X + Y x + x = 2x

i.e. A B i.e. A B i.e. P(A) P(B) [By the property of probability] i.e. F(x, x) G(2x). [Proved].

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let the random variables X and Y have joint cdf as follows: F(x,y) = {1-e^-4x-e^-5y+e^-4x-5y, x>0,...
Let the random variables X and Y have joint cdf as follows: F(x,y) = {1-e^-4x-e^-5y+e^-4x-5y, x>0, y>0 0, otherwise Find the correlation coefficient of X and Y
1. Let (X,Y ) be a pair of random variables with joint pdf given by f(x,y)...
1. Let (X,Y ) be a pair of random variables with joint pdf given by f(x,y) = 1(0 < x < 1,0 < y < 1). (a) Find P(X + Y ≤ 1). (b) Find P(|X −Y|≤ 1/2). (c) Find the joint cdf F(x,y) of (X,Y ) for all (x,y) ∈R×R. (d) Find the marginal pdf fX of X. (e) Find the marginal pdf fY of Y . (f) Find the conditional pdf f(x|y) of X|Y = y for 0...
Let X and Y have joint density f(x, y) = 6/7(x + y)^2 if 0 ≤...
Let X and Y have joint density f(x, y) = 6/7(x + y)^2 if 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, 0 otherwise, where c is a positive constant. Compute the marginal densities of X and of Y (be explicit about all cases!). Compute P(Y + 2X < 1). Determine whether X and Y are independent. Justify your answer.
Suppose a random variable X has cumulative distribution function (cdf) F and probability density function (pdf)...
Suppose a random variable X has cumulative distribution function (cdf) F and probability density function (pdf) f. Consider the random variable Y = X?b a for a > 0 and real b. (a) Let G(x) = P(Y x) denote the cdf of Y . What is the relationship between the functions G and F? Explain your answer clearly. (b) Let g(x) denote the pdf of Y . How are the two functions f and g related? Note: Here, Y is...
Let the random variable X and Y have the joint pmf f(x, y) = xy^2/c where...
Let the random variable X and Y have the joint pmf f(x, y) = xy^2/c where x = 1, 2, 3; y = 1, 2, x + y ≤ 4 , that is, (x, y) are {(1, 1),(1, 2),(2, 1),(2, 2),(3, 1)} . (a) Find c > 0 . (b) Find μX (c) Find μY (d) Find σ^2 X (e) Find σ^2 Y (f) Find Cov (X, Y ) (g) Find ρ , Corr (X, Y ) (h) Are X...
Let joint CDF Fx,y (x,y) = сxy(x2 + y2) for 0 ≤ x ≤ 1, 0...
Let joint CDF Fx,y (x,y) = сxy(x2 + y2) for 0 ≤ x ≤ 1, 0 ≤ y ≤ 1. Find а) constant с. b) Fx|y (x|y) for x = 0.5, y = 0.5.  
Let X and Y be continuous random variable with joint pdf f(x,y) = y/144 if 0...
Let X and Y be continuous random variable with joint pdf f(x,y) = y/144 if 0 < 4x < y < 12 and 0 otherwise Find Cov (X,Y).
Let X and Y have the joint pdf f(x,y) = 6*(x^2)*y for 0 <= x <=...
Let X and Y have the joint pdf f(x,y) = 6*(x^2)*y for 0 <= x <= y and x + y <= 2. What is the marginal pdf of X and Y? What is P(Y < 1.1 | X = 0.6)? Are X and Y dependent random variables?
Let X and Y have the joint probability density function f(x, y) = ⎧⎪⎪ ⎨ ⎪⎪⎩...
Let X and Y have the joint probability density function f(x, y) = ⎧⎪⎪ ⎨ ⎪⎪⎩ ke−y , if 0 ≤ x ≤ y < ∞, 0, otherwise. (a) (6pts) Find k so that f(x, y) is a valid joint p.d.f. (b) (6pts) Find the marginal p.d.f. fX(x) and fY (y). Are X and Y independent?
1. Let f : R2 → R2, f(x,y) = ?g(x,y),h(x,y)? where g,h : R2 → R....
1. Let f : R2 → R2, f(x,y) = ?g(x,y),h(x,y)? where g,h : R2 → R. Show that f is continuous at p0 ⇐⇒ both g,h are continuous at p0
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT