Timeline for Parallel independent exponential processes
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 21, 2016 at 13:36 | history | edited | Johan Falkenjack | CC BY-SA 3.0 |
Formatted math formulas latex like
|
| Dec 21, 2016 at 13:27 | vote | accept | Johan Falkenjack | ||
| Sep 16, 2015 at 15:57 | answer | added | Johan Falkenjack | timeline score: 2 | |
| Sep 16, 2015 at 15:52 | comment | added | whuber♦ | Sounds right to me. A good way to get more feedback is to post your solution as an answer, then wait for votes and comments. Incidentally, there's an easier way to obtain the expectation: integrate $1-F(x)^3$ from $0$ to $\infty$ (where $F$ is the common CDF of the $X_i$). | |
| Sep 16, 2015 at 15:14 | comment | added | Johan Falkenjack | @whuber Okay, I think I got it. P(Y<t) = P(X1<t, X2<t, X3<t)=/by independence/=P(X1<t)P(X2<t)P(X3<t). The CDF of Y would then be (1-e^(-t/5))^3. I derive this to get PDF, f(t), and calculate E(Y) the usual way by integrating t*f(t) to infinity. This gave me ~9.17 which doesn't seem unreasonable. Is my reasoning correct? | |
| Sep 16, 2015 at 12:38 | comment | added | Johan Falkenjack | @whuber I'm sorry but I'm not sure I understand. Are you saying I should construct a formula f(X1,X2,X3) = max(X1,X2,X3) and calculate it's density? | |
| Sep 15, 2015 at 20:33 | comment | added | jlimahaverford | As Whuber suggested, "the process is finished when all sub-processes are finished" leads to a mathematical description of one variable of interest, depending on these three random variables. | |
| Sep 15, 2015 at 19:54 | comment | added | whuber♦ | +1 Begin by writing down a formula for the time to completion based on the actual times needed by the three subprocesses. For instance, when those times are $1$, $8$, and $9$ minutes, your formula should give $9$ minutes. This formula, when applied to $X_1,X_2,X_3$, gives a univariate random variable. Find its distribution function (it doesn't require a triple integral), then compute the expectation. | |
| Sep 15, 2015 at 19:26 | review | First posts | |||
| Sep 15, 2015 at 19:27 | |||||
| Sep 15, 2015 at 19:21 | history | asked | Johan Falkenjack | CC BY-SA 3.0 |