Question

Let X =( X1, X2, X3 ) have the joint pdf f(x1, x2, x3)=60x1x22, where x1...

Let X =( X1, X2, X3 ) have the joint pdf f(x1, x2, x3)=60x1x22, where x1 + x2 + x3=1 and xi >0 for i = 1,2,3. find the distribution of X1 ? Find E(X1).

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
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)
(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)
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).
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...
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, X3 be a random sample from a population. The distribution of the population...
Let X1, X2, X3 be a random sample from a population. The distribution of the population has a parameter θ, and it is known that E[Xi] = 2θ and Var[Xi] = σ2 for i = 1,2,3. Consider the following two point estimators for θ: W1= (1/8)X1+ (1/4)X2+ (1/8)X3 and W2= (1/6)X1+ (1/4)X2+ (1/12)X3 Which is the better estimator for θ? Why?
Let f(x1, x2) = 1 , 0 ≤ x1 ≤ 1 , 0 ≤ x2 ≤...
Let f(x1, x2) = 1 , 0 ≤ x1 ≤ 1 , 0 ≤ x2 ≤ 1 be the joint pdf of X1 and X2 . Y1 = X1 + X2 and Y2 = X2 . (a) E(Y1) . (b) Var(Y1) (c) Consider the marginal pdf of Y1 , g(y1) . What is value of g(y1) where y1 = 1/3 and y1 = 6/4 ?
1. Consider the joint pdf f(x1,x2) = 3x1, if 0 ≤ x2 ≤ x1 ≤ 1...
1. Consider the joint pdf f(x1,x2) = 3x1, if 0 ≤ x2 ≤ x1 ≤ 1 0 elsewhere. (a) Calculate P(X1 < 3/4 ,X2 < 1/4). (b) Calculate E[3X1X2].
Let x1, x2, x3 be real numbers. The mean, x of these three numbers is defined...
Let x1, x2, x3 be real numbers. The mean, x of these three numbers is defined to be x = (x1 + x2 + x3)/3 . Prove that there exists xi with 1 ≤ i ≤ 3 such that xi ≤ x.
(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?