Consider generating a random variable Y by the following mechanism.

Nov 12th, 2015
Price: $10 USD

Question description

Consider generating a random variable Y by the following mechanism. First, generate X = x distributed as a Gamma(α, λ) random variable, then generate Y as an exponential with rate parameter x. 

  • (a)  Find P(Y<1).
  • (b)  Find the conditional distribution of X given Y = y.
  • (c)  Find the conditional expectation and variance of X given Y = y (if you carefully examine your answer for part (b), you won’t need to do any integrals).
  • (d)  Are X and Y independent random variables? Give both an intuitive and mathematical justification for your reasoning. 

Tutor Answer

(Top Tutor) ipesuni
School: University of Maryland

Studypool has helped 1,244,100 students

Review from student
" Outstanding Job!!!! "
Ask your homework questions. Receive quality answers!

Type your question here (or upload an image)

1822 tutors are online

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors