Question

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 ?

Homework Answers

Answer #1

Here a=0, b=1

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 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)
(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)
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)...
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) 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 be a sample from a uniform distribution on [0, 1] and let...
Let X1 and X2 be a sample from a uniform distribution on [0, 1] and let Y1 = min{X1, X2}, Y2 = max{X1, X2}. Find fY1 (y1|Y2 = y2). A. 1/ 2 B. 1 / 2y2 C. 1 /y2 D. 2 E. 1
Let X1 and X2 be two independent geometric random variables with the probability of success 0...
Let X1 and X2 be two independent geometric random variables with the probability of success 0 < p < 1. Find the joint probability mass function of (Y1, Y2) with its support, where Y1 = X1 + X2 and Y2 = X2.
Let X1, X2 be a sample of size 2 from the Gamma (Alpha=2, Lamba = 1/theta)...
Let X1, X2 be a sample of size 2 from the Gamma (Alpha=2, Lamba = 1/theta) distribution X1 = Gamma = x/(theta^2) e^(-x/theta) Derive the joint pdf of Y1=X1 and Y2 = X1+X2 Derive the conditional pdf of Y1 given Y2=y2. Can you name that conditional distribution? It might not have name