4. The random variables X and Y have a joint density function given by2e-2xCompute COV(X, Y).f(x, y) =X)0,if 0 ≤ x < ∞ and 0 ≤ y ≤xotherwise

Answered: Image /qna-images/answer/a969d17f-5969-4131-b18d-15e0c7b6c9b8.jpg

Answered: 4. The random variables X and Y have a…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 24EQ

See similar textbooks

Similar questions

6) The random variables X and Y have joint density f( x, y) = x2-y2 for 1< x, 1s y and f( x, y) = 0 otherwise. %3! Compute the joint density of U = X /Y and V = X Y.
Let X and Y be independent random variables with density f (x) = 3x² for 0 < x < 1. Then P (X+ Y < 1) is equal to
b) Suppose that the joint density function of random variables X₁ and X₂ is given by f(x₁, x₂)= = 0, 0< x₁ < x₂ <2 otherwise i) Draw a sketch of the area where f(x₁, x₂) is not zero. ii) Find P(X₂ < 1). iii) Find E(X₁X₂).
Suppose that the random variable X has density fx (x) = 4x³ for 0 X).
Let X and Y be two jointly continuous random variables. Let Z = X² + Y². Show that F2(=) = L Fxr(V=- yř 19) – Fxy(-v/= = y"l»)] fv (w) dy .
Let Xand Y be two continuous random variables with joint probability density [3x function given by: f(x.y)%D 0sysxsl elsewhere with E(X) = ECX)- EC) - EC*)= ;and E(XY) = 10 3 E(Y*) = - and E(XY) =; %3D Then the value of the variance of 2X+Y is: O 3/80 O 91/320 43/320 7/20
Suppose that X1, X2, and X3 are i.I.d random variables each with density function f(x)= {((1/4)x^3) if 0 < x < 2 { 0 otherwise Let the random variable M be the max of X1,X2, and X3. What is the E(M)?
5. Let X, Y be iid random variables each with density fx(x) = for x > 1 and zero otherwise. (a) (b) Find the density of Z = Y/X. Find E[√Z].
Let Y₁, Y₂,..., Yn be a random sample from the inverse Gaussian distribution with probability density function: f(y, μ, 2) = { Where μ and are unknown. a) What are i. 1 -ACT √ λ 2ny3)že elsewhere if y > 0 the likelihood ii. the log likelihood functions of u and λ. b) Find the maximum likelihood estimators of u and 2.
3. Let random variables X and Y be independent with joint density fe(x, y). Let Ix (0) and Iy (0) be the Fisher information of X and Y, respectively. Prove that the Fisher information I(x,y)(0) = Ix(0) + Iy(0).
3. Let X be a continuous random variable. Let f(x) = c(x − 1)³ and Sx = [1,3]. Hint: (x - 1)³ = x³ + 3x − 3x² - 1 (a) What value of c will make f(x) a valid density? (b) What is P(X = 2)? (c) Find E(X). (d) What is P(1 < X < 2)?
The life lengths of two transistors in an electronic circuit is a random vector (X; Y ) where X is the life length of transistor 1 and Y is the life length of transistor 2. The joint probability density function of (X; Y ) is given by | 2e-(x+2y) x 2 0, y 20 fx,y(x,y) = fx.MX.v) else Then the probability that the first transistor last for at least half hour given that the second one lasts at least half hour equals Select one: a. 0.3669 b. 0.3935 c. 0.7772 d. 0.6318 e. 0.606

SEE MORE QUESTIONS

Recommended textbooks for you

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

4. The random variables X and Y have a joint density function given by 2e-2x Compute COV(X,Y). f(x, y) = X ) 0, if 0 < x < ∞ and 0 ≤ y ≤ x otherwise