Question

LetX1 andX2 have joint density function f(x1,x2) =( 30x1x2 2, x1 −1≤ x2 ≤1−x1, 0≤ x1...

LetX1 andX2 have joint density function f(x1,x2) =( 30x1x2 2, x1 −1≤ x2 ≤1−x1, 0≤ x1 ≤10 , otherwise. (a) Find the marginal density ofX1. (b) Find the marginal density ofX2. (c) AreX1 andX2 independent?(why/why not) (d) Find the conditional density ofX2 givenX1 = x1 (e) Compute Cov(X1,X2)

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

Homework Answers

Answer #1

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
LetX1 andX2 have joint density function f(x1,x2) =( 30x1x2 2, x1 −1≤ x2 ≤1−x1, 0≤ x1...
LetX1 andX2 have joint density function f(x1,x2) =( 30x1x2 2, x1 −1≤ x2 ≤1−x1, 0≤ x1 ≤10 , otherwise. (a) Find the marginal density ofX1. (b) Find the marginal density ofX2. (c) AreX1 andX2 independent?(why/why not) (d) Find the conditional density ofX2 givenX1 = x1 (e) Compute Cov(X1,X2)
LetX1 andX2 have joint density function f(x1,x2) =( 30x1x2^2, x1 −1≤ x2 ≤1−x1, 0≤ x1 ≤10...
LetX1 andX2 have joint density function f(x1,x2) =( 30x1x2^2, x1 −1≤ x2 ≤1−x1, 0≤ x1 ≤10 , otherwise. (a) Find the marginal density of X1. (b) Find the marginal density of X2. (c) Are X1 and X2 independent?(why/why not) (d) Find the conditional density of X2 given X1 = x1 (e) Compute Cov(X1,X2)
LetX1 andX2 have joint density function f(x1,x2) =( 30x1x2^2, x1 −1≤ x2 ≤1−x1, 0≤ x1 ≤1,...
LetX1 andX2 have joint density function f(x1,x2) =( 30x1x2^2, x1 −1≤ x2 ≤1−x1, 0≤ x1 ≤1, 0 otherwise. (a) Find the marginal density of X1. (b) Find the marginal density of X2. (c) Are X1 and X2 independent?(why/why not) (d) Find the conditional density of X2 given X1 = x1 (e) Compute Cov(X1,X2)
if X1, X2 have the joint pdf f(x1, x2) = 4x1(1-x2) ,     0<x1<1 0<x2<1 and...
if X1, X2 have the joint pdf f(x1, x2) = 4x1(1-x2) ,     0<x1<1 0<x2<1 and 0,                  otherwise 1- Find the probability P(0<X1<1/3 , 0<X2<1/3) 2- For the same joint pdf, calculate E(X1X2) and E(X1 + X2) 3- Calculate Var(X1X2)
Let each of the independent random variables X1 and X2 have the density function f(x) -...
Let each of the independent random variables X1 and X2 have the density function f(x) - e^-x for 0<x< inf., and f(x) = 0, otherwise. What is the joint density of Y1 = X1 and Y2 = 2X1 + 3X2 and the domain on which this density is positive?
Let X1 and X2 have the joint pdf f(x1,x2) = 8x1x2    0<x1 <x2 <1 0....
Let X1 and X2 have the joint pdf f(x1,x2) = 8x1x2    0<x1 <x2 <1 0. elsewhere What are the marginal pdfs of x1 and x2? Find the expected values of x1 and x2. 3.   What is the expected value of X1X2? (Hint: Define g(X1, X2) = X1X2 and extend the definition of expectation of function of a random variable to two variables as follows: E[g(X1, X2)] = ? ? g(x1, x2)f(x1, x2)dx1dx2. 4. Suppose that Y = X1/X2. What...
Suppose that the joint probability density function of the random variables X and Y is f(x,...
Suppose that the joint probability density function of the random variables X and Y is f(x, y) = 8 >< >: x + cy^2 0 ≤ x ≤ 1, 0 ≤ y ≤ 1 0 otherwise. (a) Sketch the region of non-zero probability density and show that c = 3/ 2 . (b) Find P(X + Y < 1), P(X + Y = 1) and P(X + Y > 1). (c) Compute the marginal density function of X and Y...
(i) Find the marginal probability distributions for the random variables X1 and X2 with joint pdf...
(i) Find the marginal probability distributions for the random variables X1 and X2 with joint pdf                     f(x1, x2) = 12x1x2(1-x2) , 0 < x1 <1   0 < x2 < 1 , otherwise             (ii) Calculate E(X1) and E(X2)     (iii) Are the variables X1 ­and X2 stochastically independent? Given the variables in question 1, find the conditional p.d.f. of X1 given 0<x2< ½ and the conditional expectation E[X1|0<x2< ½ ].
(i) Find the probability P(0<X1<1/3 , 0<X2<1/3) where X1, X2 have the joint pdf                    f(x1, x2)...
(i) Find the probability P(0<X1<1/3 , 0<X2<1/3) where X1, X2 have the joint pdf                    f(x1, x2) = 4x1(1-x2) ,     0<x1<1  0<x2<1                                       0,                  otherwise (ii) For the same joint pdf, calculate E(X1X2) and E(X1+ X2) (iii) Calculate Var(X1X2)
Suppose that X1 and X2 are independent continuous random variables with the same probability density function...
Suppose that X1 and X2 are independent continuous random variables with the same probability density function as: f(x) = ( x 2 0 < x < 2, 0 otherwise. Let a new random variable be Y = min(X1, X2,). a) Use distribution function method to find the probability density function of Y, fY (y). b) Compute P(Y > 1). c) Compute E(Y )
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT