Problem regarding the random division

Assignment Help Basic Statistics

Reference no: EM13983804

1. Let f .x/ be the uniform density on Œ0; 1] and let g.x/ be the density on Œ0; 1] given by g.x/ Dcex , where c is the normalizing constant.

Let F; and G be the corresponding CDFs. Find the density function correspond- ing to the new CDF H.x/ D F.x/G.x/.

2. * (Random Division). Jen's dog broke off her six-inch-long pencil at a random point on the pencil. Find the density function and the expected value of the ratio of the lengths of the shorter piece and the longer piece of the pencil.

3. (Square of a PDF Need Not Be a PDF). Give an example of a density function f .x/ on Œ0; 1]such that cf 2.x/ cannot be a density function for any c.

4. (Square Root of a PDF Need Not Be a PDF). Give an example of a density function f .x/such that cpf .x/ cannot be a density function for any c.

Reference no: EM13983804

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