Question

Two students, A and B, are working independently on homework (not necessarily for the same class). Student A takes X = Exp(1) hours to finish his or her homework, while B takes Y = Exp(2) hours. (a) Find the CDF of X/Y , the ratio of their problem-solving times. (b) Find the probability that A finishes his or her homework before B does.

Answer 1

a) The CDF of X/Y is calculated as:

`F_(z) (\zeta) = (\zeta)/(\zeta + 2)` for
`0 < \zeta < \infty`

`F_(z) (\zeta) = 0` for
`\zeta \leq 0`

Note: Z = X/Y

b) Probability that A finishes before B = 1/3

Explanation:

For clarity and easiness of expression, this solution is handwritten and attached as a file. Check the complete solution in the attached file.