Stats Solutions

[Solution] Suppose that T is defined as in Definition 7.2. If W is fixed at w, then T is given by Z / c, where c=√w / v. Use this idea to find the

Question: Suppose that \(T\) is defined as in Definition 7.2.

  1. If \(W\) is fixed at \(w\), then \(T\) is given by \(Z / c\), where \(c=\sqrt{w / v}\). Use this idea to find the conditional density of \(T\) for a fixed \(W=w\)
  2. Find the joint density of \(T\) and \(W, f(t, w)\), by using \(f(t, w)=f(t \mid w) f(w)\)
  3. Integrate over \(w\) to show that
\[f(t)=\left\{\frac{\Gamma[(\nu+1) / 2]}{\sqrt{\pi v} \Gamma(\nu / 2)}\right\}\left(1+\frac{t^{2}}{\nu}\right)^{-(v+1) / 2}, \quad-\infty
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Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document


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