Statistics Solutions

[Solution Library] Let X_1 and X_2 have a joint distribution equal to the following. f(x_1, x_2)=k x_1(1+x_2) \text for 0 (5pts) Find the value of k that makes

Question: Let \(X_{1}\) and \(X_{2}\) have a joint distribution equal to the following.

\[f\left(x_{1}, x_{2}\right)=k x_{1}\left(1+x_{2}\right) \quad \text { for } 0

  1. (5pts) Find the value of \(k\) that makes this a valid joint pdf.
  2. (5pts) Are \(X_{1}\) and \(X_{2}\) independent?
  3. (5pts) Suppose we define new random variables \(Y_{1}=X_{1} / X_{2}\) and \(Y_{2}=X_{2}\). What is the joint pdf for \(Y_{1}\) and \(Y_{2} ?\) Note: If you did not determine a value of \(k\) in part
  1. , just leave your answer in terms of \(k\).
    Price: $2.99
    Solution: The downloadable solution consists of 2 pages
    Deliverable: Word Document


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