Transcribed TextTranscribed Text

3. (a) Prove that for a random variable with expectation u and variance o2, 2 lim t->0 log M(t) - t = 2/2 t2 2 (b) For a random variable X that has a chi-square distribution with 4 degrees of freedom, the moment generating function is 1 M(t) = = (1 - 2t) 2 . Use this moment generating function to show the expectation E(X) = 4. (c) Calculate the variance of X. (Thanks to part(a), there are two alternative ways to do this).

Solution PreviewSolution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

    By purchasing this solution you'll be able to access the following files:

    for this solution

    or FREE if you
    register a new account!

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

    Find A Tutor

    View available Mathematics - Other 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.

    Upload a file
    Continue without uploading

    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