Mathematics, 04.03.2020 00:29 jessnolonger

A subway has good service 70% of the time and runs less frequently 30% of the time because of signal problems. When there are signal problems, the amount of time in minutes that you have to wait at the platform is described by the pdf probability density function with signal problems = pT|SP(t) = .1e^(−.1t). But when there is good service, the amount of time you have to wait at the platform is probability density function with good service = pT|Good(t) = .3e^(−.3t) You arrive at the subway platform and you do not know if the train has signal problems or running with good service, so there is a 30% chance the train is having signal problems. (a) After 1 minute of waiting on the platform, you decide to re-calculate the probability that the train is having signal problems based on the fact that your wait will be at least 1 minute long. What is that new probability? (b) After 5 minutes of waiting, still no train. You re-calculate again. What is the new probability? (c) After 10 minutes of waiting, still no train. You re-calculate again. What is the new probability?

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Answer from: brony2199

Part a: The probability is 0.3436

Part b: The probability is 0.5381

Part c: The probability is 0.7600

Step-by-step explanation:

As per the given data

$p_{T | SP} = e^{0.1}\\p_{T | Good} = e^{0.3}\\$

(a)

Probability that train is delayed by more than 1 minute = P(T > 1) = P(SP) * P(T > 1 | SP) + P(Good) * P(T > 1 | Good)

$= 0.3 e^{-.1 \times 1 }+ 0.7 * e^{-.3 \times 1}\\ = 0.3 e^{-.1} + 0.7 e^{-.3}$

Probability that after 1 minute of waiting, probability that train has signal problems = P(SP | T > 1)

= P(T > 1 | SP) * P(SP) / P(T > 1) (By Bayes theorem)

$= \dfrac{0.3 e^{-.1 }}{ 0.3 e^{-.1 }+ 0.7 e^{-.3 }}\\\\= \dfrac{0.2714512}{0.790024}\\\\= 0.3435987$

(b)

Probability that train is delayed by more than 5 minutes = P(T > 5) = P(SP) * P(T > 5 | SP) + P(Good) * P(T > 5 | Good)

$= 0.3 e^{-.1 \times 5 }+ 0.7 * e^{-.3 \times 5}\\ = 0.3 e^{-.5} + 0.7 e^{-1.5}$

Probability that after 5 minute of waiting, probability that train has signal problems = P(SP | T > 5)

= P(T > 5 | SP) * P(SP) / P(T > 5) (By Bayes theorem)

$= \dfrac{0.3 e^{-.5 }}{ 0.3 e^{-.5 }+ 0.7 e^{-1.5 }}\\\\= \dfrac{0.1819592}{0.3381503}\\\\= 0.5381015$

(c)

Probability that train is delayed by more than 10 minutes = P(T > 10) = P(SP) * P(T > 10 | SP) + P(Good) * P(T > 10 | Good)

$= 0.3 e^{-.1 \times 10 }+ 0.7 * e^{-.3 \times 10}\\ = 0.3 e^{-1.0} + 0.7 e^{-3.0}$

Probability that after 5 minute of waiting, probability that train has signal problems = P(SP | T > 10)

= P(T > 10 | SP) * P(SP) / P(T > 10) (By Bayes theorem)

$= \dfrac{0.3 e^{-1.0 }}{ 0.3 e^{-1.0 }+ 0.7 e^{-3.0 }}\\\\= \dfrac{0.1103638}{0.1452148}\\\\= 0.7600038$

Answer from: Quest

i'm not sure what you mean but in todays world there is a lot of women that are the bread winners in the family. there is a lot more single mothers now that are going back to get an education which is boosting the economy. i believe there has been a boost in the economy due to women the cosmetic industry is boosting, chemist, the sky is becoming the limit for women in todays economy. most women are also putting off having kids just to make sure they have a education. i don't know how these two relate though to scriptures because it's not the way the lord wanted it. the man is suppose to be the bread winner and due to social media and the easy access we have there is a lot of cheating going on.

step-by-step explanation:

Answer from: Quest

step-by-step explanation:

i think because what else can be a sample of every member

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