Question

4. (i) Find the marginal probability distributions for the random variables X1 and X2 with joint...

4. (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

  1. , otherwise

            (ii) Calculate E(X1) and E(X2)    

(iii) Are the variables X1 ­and X2 stochastically independent?

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

Homework Answers

Answer #1

thank you

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
(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 0 , otherwise (ii) Calculate E(X1) and E(X2) (iii) Are the variables X1 ¬and X2 stochastically independent?
(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 ].
Let X1 and X2 be independent random variables with joint pdf f(x1, x2) =x1e^−(x1+x2), 0< x1<∞,...
Let X1 and X2 be independent random variables with joint pdf f(x1, x2) =x1e^−(x1+x2), 0< x1<∞, 0< x2<∞. Y1= 2X1 and Y2=X2−X1. I) Find g(y1, y2), the joint pdf of Y1, Y2 Include and draw the support. II) Find g1(y1), the marginal pdf of Y1. III) Find E(Y1).
(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)
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 (X1, X2) have joint pdf f(x1, x2) = (2/9)x1x22, 0 <= x1 <= 1, 0...
Let (X1, X2) have joint pdf f(x1, x2) = (2/9)x1x22, 0 <= x1 <= 1, 0 <= x2 <= 3 (i) What is the distribution of Y = X1 + X2? (ii) What is the distribution of Y = X1 * X2? (iii) Find the expectation E(X1 + X2) (iv) Find the expectation E(X1X2)
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 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 )
1. An electronic system has two different types of components in joint operation. Let X1 and...
1. An electronic system has two different types of components in joint operation. Let X1 and X2 denote the Random Length of life in hundreds of hours of the components of Type I and Type II (Type 1 and Type 2), respectively. Suppose that the joint probability density function (pdf) is given by f(x1, x2) = { (1/8)y1 e^-(x1 + x2)/2, x1 > 0, x2 > 0 0 Otherwise. a.) Show that X1 and X2 are independent. b.) Find E(Y1+Y2)...
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)
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT