Let
represent a three-dimensional vector of random variables that is uniformly distributed over the unit sphere. That is,
![](https://test.transtutors.com/qimg/de33113b-9ca5-45f3-91c9-b7314552d42c.png)
(a) Find the constant c.
(b) Find the marginal PDF for a subset of two of the three random variables. For ![](https://test.transtutors.com/qimg/b38f2f68-f170-496b-9619-1a68d22dcb31.png)
(c) Find the marginal PDF for one of the three random variables. That is, find ![](https://test.transtutors.com/qimg/1ae24c7e-9b18-44ae-ae67-373a8dbcb857.png)
(d) Find the conditional PDFs ![](https://test.transtutors.com/qimg/c8880afd-a352-4a38-9072-eba06c810b5e.png)