Statistics Solutions

(Solution Library) [20 points] Let W1 and W2 be two random variables with the joint distribution: Pr (W_1≤ w_1,W_2≤ w_2)=∫_-∞ ^w_1∫_-∞

Question: [20 points]

Let W1 and W2 be two random variables with the joint distribution:

\[\Pr \left( {{W}_{1}}\le {{w}_{1}},{{W}_{2}}\le {{w}_{2}} \right)=\int\limits_{-\infty }^{{{w}_{1}}}{\int\limits_{-\infty }^{{{w}_{2}}}{\frac{1}{2\pi }\exp \left( -\frac{1}{2}\left( {{x}^{2}}+{{y}^{2}} \right) \right)dxdy}}\]

Consider two other random variables \({{Z}_{1}}=|{{W}_{1}}|\) and \({{Z}_{2}}=|{{W}_{2}}|\). In words, Z1 is the absolute value of W1, Z2 is the absolute value of W2.

  1. [10 points] Show that Z1 is independent of Z2.
  2. [10 points] Show that Z1 and Z2 have the same distribution, and find that distribution.

Price: $2.99
Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document


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