Question

A factory produces copper wires. A blue mark is placed on a very long length of copper. The wire is then cut into pieces. The lengths of different pieces are independent, and the length of each piece is distributed according to the same PDF fX(x). Let R be length of the piece including the blue mark. Determine the expected value of R in each of the following cases. In each part below, express your answer in terms of μ using standard notation. Enter "mu" for μ.

Suppose that fX(x)={μe−μx,x≥0,0,x<0.

E[R]=

Suppose that fX(x)={μ4x3e−μx6,x≥0,0,x<0.

E[R]=

Answer 1

1. 2/mu

Answer 2

2. 5/mu