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

Answer:

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

$F_{z} (\zeta) = \frac{\zeta}{\zeta + 2}$ 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

Step-by-step explanation:

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