QuestionQuestion

Transcribed TextTranscribed Text

1. (5pts) Suppose X and Y are random variables with joint probability density function 2vxe x+y 3 f F(x,y) = , X > 0,y > 0 3VII 0, otherwise. Are X and Y independent? Explain. 2. Suppose X and Y have the joint probability function f(x,y)=(cl2x+ = y), 0, + 0 < X < 1,0 < y < 2 otherwise. a. (5pts) Find the value of C. b. (8pts) Find the marginal distribution of Y. c. (10pts) Find the joint distribution function F(x,y). 3. Suppose X and Y have joint probability density function 3y f F(x,y) = , < y < X < 2, , 4 0, otherwise. a. (10pts) Find P(Y < 1). b. (10pts) Find E(Y|X = x). c. (10pts) Find P(Y < 0.5|X=1). 4. Assume that X ~ Exp(1) and Y ~ Exp( (1) are two independent variables. Let S = Y and T = X + XY. Find a. (5pts) E (E(T|S)) b. (10pts) V(T) 5. Let Y1, Y2, , Yn be a random sample from a distribution with the probability density function y > 1 = otherwise, where 0 > 0. a. (7pts) Find the method of moments estimator of 0. b. (10pts) Find the maximum likelihood estimator for 0. 6. (10pts) Let Y1, , Y2, ,Yn , be a random sample from the uniform distribution on the interval (0, 10 - 20) where 10 < 0 < 5. Let 0 = 10 - 2Y. Show that 0 is consistent for 0. 10

Solution PreviewSolution Preview

This material may consist of step-by-step explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting. This material is made available for the sole purpose of studying and learning - misuse is strictly forbidden.

Statistics Questions
    $65.00 for this solution

    PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

    Find A Tutor

    View available Advanced Statistics Tutors

    Get College Homework Help.

    Are you sure you don't want to upload any files?

    Fast tutor response requires as much info as possible.

    Decision:
    Upload a file
    Continue without uploading

    SUBMIT YOUR HOMEWORK
    We couldn't find that subject.
    Please select the best match from the list below.

    We'll send you an email right away. If it's not in your inbox, check your spam folder.

    • 1
    • 2
    • 3
    Live Chats